Question

Write the rational expression in lowest terms. x^2-9x+8/x^2 + x-3; x^2-9x+8/x^2+2x-3 (Simplify your answer.)

Answer 1

`(x-8)/(x+3)`

Explanation:

Given expression,

`(x^2-9x+8)/(x^2+2x-3)`

`=(x^2-(8+1)x+8)/(x^2+(3-1)x-3)`

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

`=(x(x-8)-1(x-8))/(x(x+3)-1(x+3))`

`=((x-1)(x-8))/((x-1)(x+3))`

`=(x-8)/(x+3)`

Since, further simplification is not possible,

Hence, the given rational expression in lowest terms is,

`(x-8)/(x+3)`