Section 1
Simplifying Rational Expressions
When does a fraction or a rational expression equal $0 ?$
When is a fraction or a rational expression undefined?
How do you determine the value of the variable for which a rational expression is undefined?
If $x^{2}+5$ is the numerator of a rational expression, can that expression equal zero? Give a reason.
Evaluate (if possible) for a) $x=2$ and b) $x=-1$.$$\frac{7 x+1}{3 x-1}$$
Evaluate (if possible) for a) $x=2$ and b) $x=-1$.$$\frac{2\left(3 x^{2}+2\right)}{x^{2}+5 x-1}$$
Evaluate (if possible) for a) $z=-3$ and b) $z=4$.$$\frac{(2 z)^{2}}{z^{2}+5 z+6}$$
Evaluate (if possible) for a) $z=-3$ and b) $z=4$.$$\frac{2\left(z^{2}-16\right)}{z^{2}+11}$$
Evaluate (if possible) for a) $z=-3$ and b) $z=4$.$$\frac{12+4 z}{20-z^{2}}$$
Evaluate (if possible) for a) $z=-3$ and b) $z=4$.$$\frac{5 z-1}{z^{2}+z-20}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$\frac{x+2}{7 x}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$\frac{m}{m-10}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$\frac{3 r+1}{2 r-9}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$\frac{7 s+11}{5 s+11}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$\frac{10 c-c^{2}}{3 c-4}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$-\frac{z+5}{z^{2}-100}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$\frac{9}{y}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$\frac{5}{n-8}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$-\frac{7 a}{a^{2}+9 a-36}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$\frac{k-6}{k^{2}+8 k+15}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$\frac{r+10}{2 r^{2}-5 r-12}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$\frac{2}{3 d^{2}-7 d+4}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$\frac{t^{2}+8 t+15}{4 t}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$\frac{2 n-5}{9}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$\frac{4 y}{y^{2}+9}$$
Determine the value(s) of the variable for whicha) the expression equals zero.b) the expression is undefined.$$\frac{x^{2}+49}{2}$$
Write each rational expression in lowest terms.$$\frac{2 y(y-11)}{3(y-11)}$$
Write each rational expression in lowest terms.$$\frac{30(f+2)}{6(f+2)(f-5)}$$
Write each rational expression in lowest terms.$$\frac{12 d^{5}}{30 d^{8}}$$
Write each rational expression in lowest terms.$$\frac{108 g^{4}}{9 g}$$
Write each rational expression in lowest terms.$$\frac{3 c-12}{5 c-20}$$
Write each rational expression in lowest terms.$$\frac{10 d-5}{12 d-6}$$
Write each rational expression in lowest terms.$$\frac{-18 v-42}{15 v+35}$$
Write each rational expression in lowest terms.$$\frac{-12 h^{2}+15}{32 h^{2}-40}$$
Write each rational expression in lowest terms.$$\frac{39 q^{2}+26}{30 q^{2}+20}$$
Write each rational expression in lowest terms.$$\frac{3 u+15}{-7 u-35}$$
Write each rational expression in lowest terms.$$\frac{b^{2}+b-56}{b+8}$$
Write each rational expression in lowest terms.$$\frac{g^{2}+9 g+20}{g^{2}+2 g-15}$$
Write each rational expression in lowest terms.$$\frac{r-4}{r^{2}-16}$$
Write each rational expression in lowest terms.$$\frac{t+2}{t^{2}-7 t-18}$$
Write each rational expression in lowest terms.$$\frac{3 k^{2}+28 k+32}{k^{2}+10 k+16}$$
Write each rational expression in lowest terms.$$\frac{3 c^{2}-36 c+96}{c-8}$$
Write each rational expression in lowest terms.$$\frac{p^{2}-16}{2 p^{2}+7 p-4}$$
Write each rational expression in lowest terms.$$\frac{6 a^{2}-23 a+20}{4 a^{2}-25}$$
Write each rational expression in lowest terms.$$\frac{w^{3}+125}{5 w^{2}-25 w+125}$$
Write each rational expression in lowest terms.$$\frac{4 m^{3}-4}{m^{2}+m+1}$$
Write each rational expression in lowest terms.$$\frac{8 c+24}{c^{3}+27}$$
Write each rational expression in lowest terms.$$\frac{2 w^{2}+8 w+32}{w^{3}-64}$$
Write each rational expression in lowest terms.$$\frac{4 m^{2}-20 m+4 m n-20 n}{11 m+11 n}$$
Write each rational expression in lowest terms.$$\frac{u v+3 u-4 v-12}{v^{2}-9}$$
Write each rational expression in lowest terms.$$\frac{x^{2}-y^{2}}{x^{3}-y^{3}}$$
Write each rational expression in lowest terms.$$\frac{a^{3}+b^{3}}{a^{2}-b^{2}}$$
Write each rational expression in lowest terms.Any rational expression of the form $\frac{a-b}{b-a}$ reduces to what expression?
Write each rational expression in lowest terms.$$\text { Does } \frac{z+9}{z-9}=-1 ?$$
Write each rational expression in lowest terms.$$\frac{12-v}{v-12}$$
Write each rational expression in lowest terms.$$\frac{q-11}{11-q}$$
Write each rational expression in lowest terms.$$\frac{k^{2}-49}{7-k}$$
Write each rational expression in lowest terms.$$\frac{m-10}{20-2 m}$$
Write each rational expression in lowest terms.$$\frac{30-35 x}{7 x^{2}+8 x-12}$$
Write each rational expression in lowest terms.$$\frac{a^{2}-8 a-33}{11-a}$$
Write each rational expression in lowest terms.$$\frac{16-4 b^{2}}{b-2}$$
Write each rational expression in lowest terms.$$\frac{16-2 w}{w^{2}-64}$$
Write each rational expression in lowest terms.$$\frac{8 t^{3}-27}{9-4 t^{2}}$$
Write each rational expression in lowest terms.$$\frac{r^{3}-3 r^{2}+2 r-6}{21-7 r}$$
Find three equivalent forms of each rational expression.$$-\frac{b+7}{b-2}$$
Find three equivalent forms of each rational expression.$$-\frac{8 y-1}{2 y+5}$$
Find three equivalent forms of each rational expression.$$-\frac{9-5 t}{2 t-3}$$
Find three equivalent forms of each rational expression.$$\frac{-12 m}{m^{2}-3}$$
Find three equivalent forms of each rational expression.$$\frac{w-6}{-4 w+7}$$
Find three equivalent forms of each rational expression.$$\frac{-9 d-11}{10-d}$$
Reduce to lowest termsa) using long division.b) using the methods of this section.$$\frac{2 x^{2}+x-28}{x+4}$$
Reduce to lowest termsa) using long division.b) using the methods of this section.$$\frac{4 k^{2}-11 k+6}{k-2}$$
Reduce to lowest termsa) using long division.b) using the methods of this section.$$\frac{27 t^{3}-8}{3 t-2}$$
Reduce to lowest termsa) using long division.b) using the methods of this section.$$\frac{8 a^{3}+125}{2 a+5}$$
Find the missing side in each rectangle.$$\text { Area }=5 x^{2}+13 x+6$$(FIGURE CANNOT COPY)
Find the missing side in each rectangle.$$\text { Area }=2 y^{2}-y-15$$(FIGURE CANNOT COPY)
Find the missing side in each rectangle.$$\text { Area }=c^{3}-2 c^{2}+4 c-8$$(FIGURE CANNOT COPY)
Find the missing side in each rectangle.$$\text { Area }=2 n^{3}-8 n^{2}+n-4$$(FIGURE CANNOT COPY)
Determine the domain of each rational function.$$f(p)=\frac{1}{p-7}$$
Determine the domain of each rational function.$$h(z)=\frac{z+8}{z+3}$$
Determine the domain of each rational function.$$k(r)=\frac{r}{5 r+2}$$
Determine the domain of each rational function.
$$f(a)=\frac{6 a}{7-2 a}$$
Determine the domain of each rational function.$$g(t)=\frac{3 t-4}{t^{2}-9 t+8}$$
Determine the domain of each rational function.$$r(c)=\frac{c+9}{c^{2}-c-42}$$
Determine the domain of each rational function.$$h(w)=\frac{w+7}{w^{2}-81}$$
Determine the domain of each rational function.$$k(t)=\frac{t}{t^{2}-14 t+33}$$
Determine the domain of each rational function.$$A(c)=\frac{8}{c^{2}+6}$$
Determine the domain of each rational function.$$C(n)=\frac{3 n+1}{2}$$