Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Stuck on your homework problem? This step-by-step video should help.

Try Numerade Free for 30 Days

Like

Report

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.$\frac{6-\sqrt{7}}{4-\sqrt{7}}$

$\frac{17+2 \sqrt{7}}{9}$

No Related Courses

Chapter 3

REAL NUMBERS AND RADICALS

Section 7

Rationalizing a Denominator

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

02:54

Rationalize the denominato…

01:35

02:02

00:25

Rationalize each denominat…

01:21

00:29

Rationalize each numerator…

00:30

01:55

00:37

00:40

So we have six minus squared of seven over four, minus the square root of seven. So because we have this radical in our denominator here, we need to deal with that. And the only way to do that is so multiplied by the conjugated. So in this case, we have a minus. B, and it's contra get would be a plus B. So the contract is whenever you just most of pie, using the same terms that you changed the sign in the middle. So whenever you boil, we'll end up with a square minus B squared. You can boil the entire thing, but it's easier if you would just memorize this formula here. You know, just make the problem solving go by much quicker. So on the top and bottom minimal to part by four, plus the square to seven over four, plus the square to seven, so have six minus route seven times four plus Route seven all over. It was like four square minus in the square to seven years. It's on the top. We can go ahead and boil, so we have four times six. I gives us 24 six times 37 Don't give us 637 four times through something. And then our last terms of forgiveness minus seven, bring it on the bottom where square gives us 16 and then as great a seven square. It's just so, huh, are 24 months are seven now to give most 17. And because these are the same base here, wouldn't combine their coefficients. So six minus four. That gives us positive too. So have plus to Route seven in my bottom 16 minus seven gives us nine. Yeah.

View More Answers From This Book

Find Another Textbook

Rationalize the denominator and write each fraction in simplest form. All va…

Rationalize each denominator. Assume that all variables represent positive n…

Rationalize each numerator. Assume that all variables represent positive num…

Rationalize each denominator and simplify if possible.$$\frac{4 \sqrt{7}…

00:33

In $3-38$ , write each radical in simplest radical form. Variables in the ra…

00:58

01:02

In $27-39,$ factor each polynomial completely.$$12 c^{2}-3$$

00:35

02:48

In $3-38,$ solve each equation for the variable, check, and write the soluti…

01:05

02:33

Elevation of land in the United States is given by the inequality $|h-10,019…

In $3-8,$ for each function: a. Write an expression for $f(x) .$ b. Find $f(…

02:23

04:12

$$3(x-1)^{2}-12$$

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.