Find the value of!!!!!!!!!!!!!!!!!!!!!

Question

3/(x+1) - 5/(x^2-1) / (x+1)/(x-1)

Answer 1

Given 3/(x+1) - 5 / (x² -1) / (x+1) / (x-1)

Consider 3/ (x+1) - 5/(x² -1)

Rewrite expression with common denominator is (x² -1)

=(3(x - 1) - 5)/(x² -1)

=(3x - 3 - 5)/(x² -1)

=(3x - 8)/(x² -1)

Then (3x - 8)/(x² -1)/(x+1)/(x -1) 

 =(3x - 8)/(x+1)(x -1) / (x+1)/(x -1)              ( By the mathematical index formula (a+b) (a-b)=a²-b²

Cancel the  common terms in nominator and denominator

=3x - 8/(x+1)(x + 1)

=3x - 8/(x+1)²

Therefore 3/(x+1)-5/(x² -1)/(x+1)/(x -1)= 3x - 8/(x+1)²

Answer 2

The rational expression is

Difference of two squares  a ²- b ² = (a + b ) (a - b )

In this case a = x , b = 1

 

Cancel the  common terms in numerator and denominator.