Simplify 1/(x-4)*(-x^2+9x-20)/(x+2)

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

Step 1

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = - 1 \cdot - 20 = 20$ and whose sum is $b = 9$ .

Factor $9$ out of $9 x$ .

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

Rewrite $9$ as $4$ plus $5$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $- x + 4$ .

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

Step 2

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

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

Step 3

Cancel the common factor of $- x + 4$ and $x - 4$ .

Factor $- 1$ out of $- x$ .

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

Rewrite $4$ as $- 1 (- 4)$ .

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

Factor $- 1$ out of $- (x) - 1 (- 4)$ .

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

Rewrite $- (x - 4)$ as $- 1 (x - 4)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Move the negative in front of the fraction.

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

Simplify 1/(x-4)*(-x^2+9x-20)/(x+2)

Related Questions

Support LCMGCF.com by disabling your adblocker.