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Elementary Algebra

Lynn Marecek

Chapter 8

Rational Expressions and Equations - all with Video Answers

Educators

Section 1

Simplify Rational Expressions

02:27

Problem 1

In the following exercises, determine the values for which the rational expression is undefined.
(a) $\frac{2 x}{z}$
(b) $\frac{4 p-1}{6 p-5}$
(c) $\frac{n-3}{n^{2}+2 n-8}$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:35

Problem 2

In the following exercises, determine the values for which the rational expression is undefined.
(a) $\frac{10 m}{11 n}$ (b) $\frac{6 y+13}{4 y-9}$
(c) $\frac{b-8}{b^{2}-36}$

Suzanne Harwood
Suzanne Harwood
Numerade Educator
03:48

Problem 3

In the following exercises, determine the values for which the rational expression is undefined.
(a) $\frac{10 m}{11 n}$ (b) $\frac{6 y+13}{4 y-9}$ (c) $\frac{b-8}{b^{2}-36}$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:20

Problem 4

In the following exercises, determine the values for which the rational expression is undefined.
(a) $\frac{5 p q^{2}}{9 q}$ (b) $\frac{7 a-4}{3 a+5}$ ( c$) \frac{1}{x^{2}-4}$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:18

Problem 5

In the following exercises, evaluate the rational expression for the given values.
$\frac{2 x}{x-1}$
(b) $x=2$
(a) $x=0$
(c) $x=-1$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:37

Problem 6

In the following exercises, evaluate the rational expression for the given values.
$\frac{4 y-1}{5 y-3}$
(a) $y=0$
(b) $y=2$
(c) $y=-1$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:44

Problem 7

In the following exercises, evaluate the rational expression for the given values.
$\frac{2 p+3}{p^{2}+1}$
(a) $p=0$
(b) $p=1$
(c) $p=-2$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:58

Problem 8

In the following exercises, evaluate the rational expression for the given values.
$\frac{x+3}{2-3 x}$
(a) $x=0$ (b) $x=1$ (c) $x=-2$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:49

Problem 9

In the following exercises, evaluate the rational expression for the given values.
$\frac{y^{2}+5 y+6}{y^{2}-1}$
(a) $y=0$
(b) $y=2$
(c) $y=-2$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:20

Problem 10

In the following exercises, evaluate the rational expression for the given values.
$\frac{z^{2}+3 z-10}{z^{2}-1}$
(a) $z=0$
(b) $z=2$
c) $z=-2$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:39

Problem 11

In the following exercises, evaluate the rational expression for the given values.
$\frac{a^{2}-4}{a^{2}+5 a+4}$
(a) $a=0$ (b) $a=1$ (c) $a=-2$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:37

Problem 12

In the following exercises, evaluate the rational expression for the given values.
$\frac{b^{2}+2}{b^{2}-3 b-4}$
(a) $b=0$
(b) $b=2$
c) $b=-2$

Chris Wojturski
Chris Wojturski
Numerade Educator
05:34

Problem 13

In the following exercises, evaluate the rational expression for the given values.
$\frac{x^{2}+3 x y+2 y^{2}}{2 x^{3} y}$
(a) $x=1, y=-1$
(b) $x=2, y=1$
(c) $x=-1, y=-2$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:58

Problem 14

In the following exercises, evaluate the rational expression for the given values.
$\frac{c^{2}+c d-2 d^{2}}{c d^{3}}$
(a) $c=2, d=-1$
(b) $c=1, d=-1$
(c) $c=-1, d=2$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:39

Problem 15

In the following exercises, evaluate the rational expression for the given values.
$\frac{m^{2}-4 n^{2}}{5 m n^{3}}$
(a) $m=2, n=1$
(b) $m=-1, n=-1$
(c) $m=3, n=2$

Chris Wojturski
Chris Wojturski
Numerade Educator
04:01

Problem 16

In the following exercises, evaluate the rational expression for the given values.
$\frac{2 s^{2} t}{s^{2}-9 t^{2}}$
(a) $s=4, t=1$
(b) $s=-1, t=-1$
c) $s=0, t=2$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:05

Problem 17

In the following exercises, simplify.
$$
-\frac{4}{52}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:02

Problem 18

In the following exercises, simplify.
$$
-\frac{44}{55}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:30

Problem 19

In the following exercises, simplify.
$$
\frac{56}{63}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:58

Problem 20

In the following exercises, simplify.
$$
-\frac{44}{55}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:23

Problem 21

In the following exercises, simplify.
$$
\frac{6 a b^{2}}{12 a^{2} b}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:08

Problem 22

In the following exercises, simplify.
$$
\frac{15 x y}{3 x^{3} y^{3}}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:10

Problem 23

In the following exercises, simplify.
$$
\frac{8 m^{3} n}{12 m n^{2}}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:06

Problem 24

In the following exercises, simplify.
$$
\frac{36 v^{3} w^{2}}{27 v w^{3}}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:31

Problem 25

In the following exercises, simplify.
$$
\frac{3 a+6}{4 a+8}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:40

Problem 26

In the following exercises, simplify.
$$
\frac{5 b+5}{6 b+6}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:53

Problem 27

In the following exercises, simplify.
$$
\frac{3 c-9}{5 c-15}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:02

Problem 28

In the following exercises, simplify.
$$
\frac{4 d+8}{9 d+18}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:18

Problem 29

In the following exercises, simplify.
$$
\frac{7 m+63}{5 m+45}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:54

Problem 30

In the following exercises, simplify.
$$
\frac{8 n-96}{3 n-36}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:12

Problem 31

In the following exercises, simplify.
$$
\frac{12 p-240}{5 p-100}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:50

Problem 32

In the following exercises, simplify.
$$
\frac{6 q+210}{5 q+175}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:29

Problem 33

In the following exercises, simplify.
$$
\frac{a^{2}-a-12}{a^{2}-8 a+16}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:01

Problem 34

In the following exercises, simplify.
$$
\frac{x^{2}+4 x-5}{x^{2}-2 x+1}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:23

Problem 35

In the following exercises, simplify.
$$
\frac{y^{2}+3 y-4}{y^{2}-6 y+5}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:52

Problem 36

In the following exercises, simplify.
$$
\frac{v^{2}+8 v+15}{v^{2}-v-12}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:48

Problem 37

In the following exercises, simplify.
$$
\frac{x^{2}-25}{x^{2}+2 x-15}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:48

Problem 38

In the following exercises, simplify.
$$
\frac{a^{2}-4}{a^{2}+6 a-16}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:50

Problem 39

In the following exercises, simplify.
$$
\frac{y^{2}-2 y-3}{y^{2}-9}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
01:50

Problem 40

In the following exercises, simplify.
$$
\frac{b^{2}+9 b+18}{b^{2}-36}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:28

Problem 41

In the following exercises, simplify.
$$
\frac{y^{3}+y^{2}+y+1}{y^{2}+2 y+1}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:31

Problem 42

In the following exercises, simplify.
$$
\frac{p^{3}+3 p^{2}+4 p+12}{p^{2}+p-6}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
04:07

Problem 43

In the following exercises, simplify.
$$
\frac{x^{3}-2 x^{2}-25 x+50}{x^{2}-25}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
03:30

Problem 44

In the following exercises, simplify.
$$
\frac{q^{3}+3 q^{2}-4 q-12}{q^{2}-4}
$$

Chris Wojturski
Chris Wojturski
Numerade Educator
02:40

Problem 45

In the following exercises, simplify.
$$
\frac{3 a^{2}+15 a}{6 a^{2}+6 a-36}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
02:09

Problem 46

In the following exercises, simplify.
$$
\frac{8 b^{2}-32 b}{2 b^{2}-6 b-80}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
02:28

Problem 47

In the following exercises, simplify.
$$
\frac{-5 c^{2}-10 c}{-10 c^{2}+30 c+100}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
01:52

Problem 48

In the following exercises, simplify.
$$
\frac{4 d^{2}-24 d}{2 d^{2}-4 d-48}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
02:16

Problem 49

In the following exercises, simplify.
$$
\frac{3 m^{2}+30 m+75}{4 m^{2}-100}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
02:25

Problem 50

In the following exercises, simplify.
$$
\frac{5 n^{2}+30 n+45}{2 n^{2}-18}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
01:46

Problem 51

In the following exercises, simplify.
$$
\frac{5 r^{2}+30 r-35}{r^{2}-49}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
02:09

Problem 52

In the following exercises, simplify.
$$
\frac{3 s^{2}+30 s+72}{3 s^{2}-48}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
01:34

Problem 53

In the following exercises, simplify.
$$
\frac{t^{3}-27}{t^{2}-9}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
01:21

Problem 54

In the following exercises, simplify.
$$
\frac{v^{3}-1}{v^{2}-1}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
01:22

Problem 55

In the following exercises, simplify.
$$
\frac{w^{3}+216}{w^{2}-36}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
01:10

Problem 56

In the following exercises, simplify.
$$
\frac{v^{3}+125}{v^{2}-25}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
01:23

Problem 57

In the following exercises, simplify each rational expression.
$$
\frac{a-5}{5-a}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
01:25

Problem 58

In the following exercises, simplify each rational expression.
$$
\frac{b-12}{12-b}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
01:19

Problem 59

In the following exercises, simplify each rational expression.
$$
\frac{11-c}{c-11}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
01:10

Problem 60

In the following exercises, simplify each rational expression.
$$
\frac{5-d}{d-5}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
01:53

Problem 61

In the following exercises, simplify each rational expression.
$$
\frac{12-2 x}{x^{2}-36}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
01:43

Problem 62

In the following exercises, simplify each rational expression.
$$
\frac{20-5 y}{y^{2}-16}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
02:58

Problem 63

In the following exercises, simplify each rational expression.
$$
\frac{4 v-32}{64-v^{2}}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
02:23

Problem 64

In the following exercises, simplify each rational expression.
$$
\frac{7 w-21}{9-w^{2}}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
02:28

Problem 65

In the following exercises, simplify each rational expression.
$$
\frac{y^{2}-11 y+24}{9-y^{2}}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
02:16

Problem 66

In the following exercises, simplify each rational expression.
$$
\frac{z^{2}-9 z+20}{16-z^{2}}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
02:12

Problem 67

In the following exercises, simplify each rational expression.
$$
\frac{a^{2}-5 a-36}{81-a^{2}}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
01:53

Problem 68

In the following exercises, simplify each rational expression.
$$
\frac{b^{2}+b-42}{36-b^{2}}
$$

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
03:20

Problem 69

Tax Rates For the tax year $2015,$ the amount of tax owed by a single person earning between $\$ 37,450$ and $\$ 90,750$, can be found by evaluating the formula $0.25 x-4206.25,$ where $x$ is income. The average tax rate for this income can be found by evaluating the formula $\frac{0.25 x-4206.25}{x} .$ What would be the average tax rate for a single person earning $\$ 50,000 ?$

Gokul R Nair
Gokul R Nair
Numerade Educator
02:29

Problem 70

Work The length of time it takes for two people for perform the same task if they work together can be found by evaluating the formula $\frac{x y}{x+y}$. If Tom can paint the den in $x=45$ minutes and his brother Bobby can paint it in $y=60$ minutes, how many minutes will it take them if they work together?

Gokul R Nair
Gokul R Nair
Numerade Educator
02:33

Problem 71

Explain how you find the values of $x$ for which the rational expression $\frac{x^{2}-x-20}{x^{2}-4}$ is undefined.

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator
02:24

Problem 72

Explain all the steps you take to simplify the rational expression $\frac{p^{2}+4 p-21}{9-p^{2}}$.

Katelyn Vandeaver
Katelyn Vandeaver
Numerade Educator