What is (8x^2-36x-72)/(6-x) ?

The solution to (8x^2-36x-72)/(6-x) is -8x-12

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simplify (8x^2-36x-72)/(6-x)

simplify

\frac{8 x ^{2} - 36 x - 72}{6 - x}

- 8 x - 12

Solution steps

\frac{8 x ^{2} - 36 x - 72}{6 - x}

Factor

8 x^{2} - 36 x - 72 : 4 (2 x^{2} - 9 x - 18)

= \frac{4 ( 2 x ^{2} - 9 x - 18 )}{6 - x}

Factor

2 x^{2} - 9 x - 18 : (2 x + 3) (x - 6)

= \frac{4 ( 2 x + 3 ) ( x - 6 )}{6 - x}

6 - x = - (x - 6)

= \frac{4 ( 2 x + 3 ) ( x - 6 )}{- ( x - 6 )}

Cancel the common factor:

x - 6

= \frac{4 ( 2 x + 3 )}{- 1}

Apply the fraction rule:

\frac{a}{- 1} = - a

= - 4 (2 x + 3)

Expand

- 4 (2 x + 3) : - 8 x - 12

= - 8 x - 12

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

2 + (- \frac{1}{4})

44 n + 20 n^{2} - 15

- 2 \frac{5}{6}

(- 8) (12)