Question

(1/x-4)• (-x^2+9x-20/x+2) (Multiplying And Dividing Rational Expressions)

Answer 1

ANSWER

$\frac{5 - x}{x + 2}$

EXPLANATION

We want to simplify the rational expression:

$( \frac{1}{x - 4)} )( \frac{ - {x}^{2} + 9x - 20}{x + 2} )$

We split the middle term to obtain:

$( \frac{1}{x - 4)} )( \frac{ - {x}^{2} + 5x + 4x- 20}{x + 2} )$

We now factor to obtain;

$( \frac{1}{x - 4)} )( \frac{-x(x - 5) + 4(x - 5)}{x + 2} )$

$( \frac{1}{x - 4)} )( \frac{(x - 5)(4 - x)}{x + 2} )$

Or

$( \frac{1}{x - 4)} ) ( \frac{ - (x - 5)(x - 4)}{x + 2} )$

We cancel the common factors to get;

$\frac{ - (x - 5)}{x + 2}$

$= \frac{5 - x}{x + 2}$