Question

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

Answer 1

`(5 - x)/(x + 2)`

Step-by-step explanation

We want to simplify the rational expression:

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

We split the middle term to obtain:

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

We now factor to obtain;

`( (1)/(x - 4)) )( (-x(x - 5) + 4(x - 5))/(x + 2) )`

`( (1)/(x - 4)) )( ((x - 5)(4 - x))/(x + 2) )`

Or

`( (1)/(x - 4)) ) ( ( - (x - 5)(x - 4))/(x + 2) )`

We cancel the common factors to get;

`( - (x - 5))/(x + 2)`

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