SOLUTION: Show that each equattion is true by simplifying the following: a.) {{{1/(sqrt(x)+sqrt(y)) = (sqrt(x)-sqrt(y))/(x-y)}}} b.) {{{(sqrt(x+h)- sqrt(x))/h = 1/(sqrt(x+h)+sqrt(x)

Algebra ->  Radicals -> SOLUTION: Show that each equattion is true by simplifying the following: a.) {{{1/(sqrt(x)+sqrt(y)) = (sqrt(x)-sqrt(y))/(x-y)}}} b.) {{{(sqrt(x+h)- sqrt(x))/h = 1/(sqrt(x+h)+sqrt(x)      Log On


   

Question 47824: Show that each equattion is true by simplifying the following:

a.) 1%2F%28sqrt%28x%29%2Bsqrt%28y%29%29+=+%28sqrt%28x%29-sqrt%28y%29%29%2F%28x-y%29
b.) %28sqrt%28x%2Bh%29-+sqrt%28x%29%29%2Fh+=+1%2F%28sqrt%28x%2Bh%29%2Bsqrt%28x%29%29

can someone PLEASE help me with this? any help will be appreciated!!!
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Show that each equattion is true by simplifying the following:
USE A^-B^2=(A+B)(A-B)...RATIONALISE THE IRRATIONAL N.R....OR...D.R BY MULTIPLYING WITH CONJUGATE FACTOR.
a.) 1/(sqrt(x)+sqrt(y)) = (sqrt(x)-sqrt(y))/(x-y)
MULTIPLY N.R AND D.R WITH {SQRT(X)-SQRT(Y)}
{SQRT(X)-SQRT(Y)}/[{SQRT(X)}^2-{SQRT(Y)}^2]=(sqrt(x)-sqrt(y))/(x-y)
b.) (sqrt(x+h)- sqrt(x))/h = 1/(sqrt(x+h)+sqrt(x))
SAME WAY AS ABOVE ..MULTIPLY N.R AND D.R WITH (sqrt(x+h)+ sqrt(x))