resolute (1/2(x+1)) + [1/2(x-1)]

Question

instead of resolving into partial fractions . resolute the partial fraction back to its original form

Answer 1

resolute (1/2(x+1)) + [1/2(x-1)]

instead of resolving into partial fractions . resolute the partial fraction back to its original form.

We have,

 (1/2(x+1)) + [1/2(x-1)] =

(1/2)[1/(x + 1) + 1/(x - 1)] =     multiply both terms by 1

(1/2)[1/(x + 1)*{(x - 1)/(x - 1)} + 1/(x - 1)*{(x + 1)/(x + 1)}] =

(1/2)[(x - 1) / {(x + 1)(x - 1)} + (x + 1) / {(x - 1)(x + 1)}]

(1/2)[(x - 1) / (x^2 - 1) + (x + 1) / (x^2 - 1)] =

(1/[2(x^2 - 1)])[(x - 1) + (x + 1)] =

(1/[2(x^2 - 1)])[2x] =

(2x/[2(x^2 - 1)]) =

x/(x^2 - 1)

Answer: x/(x^2 - 1)