Algebra Help?

PROBLEM 1:

√5
---
√7

To rationalize the denominator, you need to multiply by √7 on top and bottom:
√5 .. √7 .. √35 .. √35
--- x ---- = ----- = ----
√7 .. √7 .. √49 .... 7

PROBLEM 2:

I'm going to assume the second part is all in the denominator as opposed to (√2/√3) - √7

... √2
----------
√3 - √7

Here you want to multiply by √3 + √7 on top and bottom. Notice that if it is a subtraction of radicals, you want to multiply by the addition of those same radicals.

... √2 ...... √3 + √7 ................ √6 + √14 ................... √6 + √14
---------- x ------------ = ----------------------------------- = ---------------
√3 - √7 ... √3 + √7 .... (√3)² + √7√3 - √7√3 - (√7)² ... (√3)² - (√7)²

√6 + √14
------------
... 3 - 7

Answer:
√6 + √14
------------
..... -4

1)
sqrt(5)/sqrt(7)

sqrt(35)/7

2)
sqrt(2) / (sqrt(3) - sqrt(7))

sqrt(2)(sqrt(3)-sqrt(7)) / (3-7)

(sqrt(6) - sqrt(14)) / -4

(√5)/(√7) × (√7)/(√7) = (√(5×7))/7 = (√35)/7
:::::
What is the denominator? √3, or √3 - √7 ?

1-√5/√3(√3/√3)
√3(1-√5)/3