SOLUTION: Subtract the rational expression. 1 over 5-x minus 4 over 5+x

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Question 174888This question is from textbook saxon algebra 2
: Subtract the rational expression.
1 over 5-x minus 4 over 5+x This question is from textbook saxon algebra 2

Answer by actuary(112) About Me  (Show Source):
You can put this solution on YOUR website!
The first thing that needs to be done is to put both fractional expressions over a common denominator:
{1/(5-x)}-{ 4/(5+x)} = (5+x)/{(5-x)*(5+x)}-4*(5-x)/{(5-x)*(5+x)}
Then subtract the two fractional expressions
Finally, simplify both the numerator and the denominator
= {(5+x)-4*(5-x)}/{(5-x)*(5+x)}= (5+x-20+4x)/(25-x^2)=(5x-15)/(25-x^2)
=5*(x-3)/(25-x^2)