## anonymous one year ago rationalize the denominator and simplify (2√7+3)/(√7+2)

1. anonymous

When you want to rationalize the denominator you want to multiply it by the numerator and denominator by the conjugate $\sqrt{7}-2$

2. anonymous

$\frac{ (2\sqrt{7}+3 )}{ (\sqrt{7}+2 )} \times \frac{ \sqrt{7}-2 }{ \sqrt{7}-2 }$

3. anonymous

why is it negative? shouldnt it be positive 2?

4. anonymous

oh opps just kidding the bottom cancels out

5. anonymous

To rationalize we use the conjugate which simply means we change the sign so notice how we want to rationalize the denominator so we multiply the top and bottom by sqrt(7)-2 we change the + to - this way we can get an expression as such $a^2-b^2$

6. anonymous

Yeah!

7. UsukiDoll

"When you want to rationalize the denominator you want to multiply it by the numerator and denominator by the conjugate " signs need to be switched.. since you have a + on the denominator we have to multiply by sqrt{7}-2

8. anonymous

ahaha I understand now! thank you both!