Rational expression math help?

if we subtract the fractions

6/x^2-1 - 1/x+1= 1/2...

we can factorize x^2-1 into (x+1)(x-1) which is known as the difference between 2 squares

6/(x+1)(x-1) -1/x+1=1/2

we can take (x+1)(x-1) to be the lowest common denominator and we can solve it

6-1(x-1)/(x+1)(x-1)=1/2. Because the 1/x+1 term was missing x-1 from it's denominator we had to cross multiply it on the numerator to balance things.

this tidies up to give:

7-x/(x+1)(x-1)=1/2

we can now multiply by (x+1)(x-1) to get rid of the denominator

7-x= 1/2(x+1)(x-1)

multiplying both sides by 2

14-2x=(x+1)(x-1)

expanding

14-x=x^2-1

subtracting both sides by 14-x

x^2+2x-15=0

(x+5)(x-3)=0

x+5=0, x=-5

x-3=0, x=3

so indeed x=3 but you missed the value x=-5. which would have costed you some marks as your answer isn't entirely correct :)