What is (-4x-32)/(x^2-12x+36)*(x^2-9x+18)/(3x+24) ?

The solution to (-4x-32)/(x^2-12x+36)*(x^2-9x+18)/(3x+24) is -(4(x-3))/(3(x-6))

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simplify (-4x-32)/(x^2-12x+36)*(x^2-9x+18)/(3x+24)

simplify

\frac{- 4 x - 32}{x ^{2} - 12 x + 36} \cdot \frac{x ^{2} - 9 x + 18}{3 x + 24}

- \frac{4 ( x - 3 )}{3 ( x - 6 )}

Solution steps

\frac{- 4 x - 32}{x ^{2} - 12 x + 36} \cdot \frac{x ^{2} - 9 x + 18}{3 x + 24}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{( - 4 x - 32 ) ( x ^{2} - 9 x + 18 )}{( x ^{2} - 12 x + 36 ) ( 3 x + 24 )}

Factor

- 4 x - 32 : - 4 (x + 8)

= \frac{- 4 ( x + 8 ) ( x ^{2} - 9 x + 18 )}{( x ^{2} - 12 x + 36 ) ( 3 x + 24 )}

Factor

3 x + 24 : 3 (x + 8)

= \frac{- 4 ( x + 8 ) ( x ^{2} - 9 x + 18 )}{( x ^{2} - 12 x + 36 ) \cdot 3 ( x + 8 )}

Cancel the common factor:

x + 8

= \frac{- 4 ( x ^{2} - 9 x + 18 )}{( x ^{2} - 12 x + 36 ) \cdot 3}

Factor

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

= \frac{- 4 ( x - 3 ) ( x - 6 )}{( x ^{2} - 12 x + 36 ) \cdot 3}

Factor

x^{2} - 12 x + 36 : (x - 6)^{2}

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x - 6)^{2} = (x - 6) (x - 6)

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

Cancel the common factor:

x - 6

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

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

(x - 8) (x - 11)

x + 2 x + 3 x

\frac{\frac{4}{3}}{\frac{2}{3}}

\frac{15 r ^{6} c ^{- 8}}{( 3 r ^{- 3} c ) ^{- 5}}

(4^{6})^{3}

What is (-4x-32)/(x^2-12x+36)*(x^2-9x+18)/(3x+24) ?
The solution to (-4x-32)/(x^2-12x+36)*(x^2-9x+18)/(3x+24) is -(4(x-3))/(3(x-6))