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

Answer:

$\frac{x-8}{x+3}$

Step-by-step explanation:

Given expression,

$\frac{x^2-9x+8}{x^2+2x-3}$

$=\frac{x^2-(8+1)x+8}{x^2+(3-1)x-3}$

$=\frac{x^2-8x-x+8}{x^2+3x-x-3}$

$=\frac{x(x-8)-1(x-8)}{x(x+3)-1(x+3)}$

$=\frac{(x-1)(x-8)}{(x-1)(x+3)}$

$=\frac{x-8}{x+3}$

Since, further simplification is not possible,

Hence, the given rational expression in lowest terms is,

$\frac{x-8}{x+3}$