SOLUTION: Can someone help me with this i've tried and i am not ending up with the right solutions. "Show that each equation is TRUE by SIMPLIFYING the following:" a.) {{{1/(sqrt(x)+sqrt(

Algebra ->  Equations -> SOLUTION: Can someone help me with this i've tried and i am not ending up with the right solutions. "Show that each equation is TRUE by SIMPLIFYING the following:" a.) {{{1/(sqrt(x)+sqrt(      Log On


   

Question 48421: Can someone help me with this i've tried and i am not ending up with the right solutions.
"Show that each equation 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
c.) %28x-y%29%2F%28sqrt%28x%29%2Bsqrt%28y%29%29=sqrt%28x%29-sqrt%28y%29
d.) %28sqrt%28x%2B4%29-2%29%2Fx=1%2F%28sqrt%28x%2B4%29%2B2%29
Please help i dont understand how to show that the equation is true by simplifying, i've tried but nothing i've done has came out right.
Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
What is happening here is that the numerators and the denominators are being multiplied by the conjuate of the radical. The conjugate causes the elimination of the radical. It is the same as the difference of two squares:
%28a%5E2-b%5E2%29 = (a-b)(a+b)
(a-b) is the conjugate of (a+b) and (a+b) is the conjugate of (a-b).
.
a.) 1%2F%28sqrt%28x%29%2Bsqrt%28y%29%29=%28sqrt%28x%29-sqrt%28y%29%29%2F%28x-y%29
[Multiply the numerator and denominator by the conjugate of
(sqrt(x)+ sqrt(y)) which is (sqrt(x)- sqrt(y))
.
1(sqrt(x)-sqrt(y)/(sqrt(x)+ sqrt(y)(sqrt(x)- sqrt(y)
When you multiply a square root by itself, the radical sign cancels out:
Example: (sqrt(3)(sqrt(3)= sqrt(9)= 3
.
Cancel if possible:
1(sqrt(x)- sqrt(y)/(x)-(y)
.
(sqrt(x)- sqrt(y)/x-y