What is (x^2-x-30)/(5x+40)*(3x+6)/(x^2+7x+10) ?

The solution to (x^2-x-30)/(5x+40)*(3x+6)/(x^2+7x+10) is (3(x-6))/(5x+40)

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simplify (x^2-x-30)/(5x+40)*(3x+6)/(x^2+7x+10)

simplify

\frac{x ^{2} - x - 30}{5 x + 40} \cdot \frac{3 x + 6}{x ^{2} + 7 x + 10}

\frac{3 ( x - 6 )}{5 x + 40}

Solution steps

\frac{x ^{2} - x - 30}{5 x + 40} \cdot \frac{3 x + 6}{x ^{2} + 7 x + 10}

Cancel

\frac{3 x + 6}{x ^{2} + 7 x + 10} : \frac{3}{x + 5}

= \frac{x ^{2} - x - 30}{5 x + 40} \cdot \frac{3}{x + 5}

Apply the fraction rule:

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

= \frac{( x ^{2} - x - 30 ) \cdot 3}{( 5 x + 40 ) ( x + 5 )}

Factor

x^{2} - x - 30 : (x + 5) (x - 6)

= \frac{( x + 5 ) ( x - 6 ) \cdot 3}{( 5 x + 40 ) ( x + 5 )}

Cancel the common factor:

x + 5

= \frac{( x - 6 ) \cdot 3}{5 x + 40}

= \frac{3 ( x - 6 )}{5 x + 40}

\frac{2}{5} \times \frac{1}{4}

(m + 6) (m - 6)

\frac{( x ^{3} + 8 )}{( x + 2 )}

(7 a^{2} - b) (3 a - 2 b)

\frac{3 x + 18}{x ^{2} + 6 x}

What is (x^2-x-30)/(5x+40)*(3x+6)/(x^2+7x+10) ?
The solution to (x^2-x-30)/(5x+40)*(3x+6)/(x^2+7x+10) is (3(x-6))/(5x+40)