Question

How do you simplify `(4x-1)/(x^2-4) - (3(x-1))/(x-2)`?

Answer 1

`=(-3x^2+x+5)/((x+2)(x-2))`

Explanation:

Before you can subtract fractions you must have a common denominator. In algebraic fractions you will often have to factorise first.

`(4x-1)/(x^2-4) -(3(x-1))/(x-2)`

`=color(blue)((4x-1)/((x+2)(x-2))) -(3(x-1))/(x-2)" "larr`LCD = `(x+2)(x-2)`
`color(white)(xxxxxx)darrcolor(white)(xxxxxxxxxx)darr`
`color(blue)("stays the same") color(white)(xxxx\x) xx color(red)((x+2)/(x+2))`

`=(color(blue)(4x-1) color(red)(-3(x-1)(x+2)))/((x+2)(x-2))`

`=(4x-1-color(red)(3(x^2+x-2)))/((x+2)(x-2))`

`=(4x-1-color(red)(3x^2-3x+6))/((x+2)(x-2))`

`=(-3x^2+x+5)/((x+2)(x-2))`