Question

`2-(x+1)/(x-2) -(x-4)/(x+2)` can be written as a single fraction in the form
`(ax+b)/(x^(2) -4)` where a and b are integers.

work out the value of a, and the value of b

Answer 1

a = 3 , b = - 18

Explanation:

2 -
`(x+1)/(x-2)` -
`(x-4)/(x+2)`

express as a fraction with common denominator (x - 2)(x + 2)

=
`(2(x-2)(x+2)-(x+1)(x+2)-(x-4)(x-2))/((x-2)(x+2))`

=
`(2(x^2-4)-(x^2+3x+2)-(x^2-6x+8))/(x^2-4)`

=
`(2x^2-8-x^2-3x-2-x^2+6x-8)/(x^2-4)`

=
`(3x-18)/(x^2-4)`

compare to
`(ax+b)/(x^2-4)`

with a = 3 and b = - 18