How do you simplify x/(x^2-16) + (x-2)/(x^2-5x+4)xx216+x2x25x+4?

1 Answer
Jun 15, 2018

(2x^2+x-8)/((x-4)(x+4)(x-1))2x2+x8(x4)(x+4)(x1)

Explanation:

Note that

x^2-16=(x-4)(x+4)x216=(x4)(x+4)

x^2-5x+4=(x-4)(x-1)x25x+4=(x4)(x1)
so we have to add

(x(x-1))/((x-4)(x+4)(x-1))x(x1)(x4)(x+4)(x1)

((x-2)(x+4))/((x-4)(x-1)(x+4))(x2)(x+4)(x4)(x1)(x+4)
and we have

x(x-1)=x^2-xx(x1)=x2x

(x-2)(x+4)=x^2+2x-8(x2)(x+4)=x2+2x8
so we get the result above.