Question

Which of the following is equivalent to x/x^2-1 + 4/x^2-6x-7?

a. x(x-7)+4(x-1)/(x+1)^2(x-7)
b. x+4/(x+1)^2(x-7)
c. x(x-7)+4(x-1)/(x+1)(x-1)(x-7)
d. x+4/(x+1)(x-1)(x-7)

Answer 1

x(x-7)+4(x-1)/(x-1)(x+1)(x-7)

Explanation:

Given the expression x/x²-1 + 4/x²-6x-7

Factorize x²-6x-7

x²-6x-7

= x²-7x+x-7

= x(x-7)+1(x-7)

= (x+1)(x-7)

Replace back into the expression given

x/x²-1 + 4/x²-6x-7

= x/x²-1 + 4/ (x+1)(x-7)

= x/(x+1)(x-1) + 4/(x+1)(x-7)

Find the LCM

= x(x-7)+4(x-1)/(x-1)(x+1)(x-7)

This gives the required expression