What is (6x-60)/(x^3+3x^2)*(x^3-9x)/(x^2-13x+30) ?

The solution to (6x-60)/(x^3+3x^2)*(x^3-9x)/(x^2-13x+30) is 6/x

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simplify (6x-60)/(x^3+3x^2)*(x^3-9x)/(x^2-13x+30)

simplify

\frac{6 x - 60}{x ^{3} + 3 x ^{2}} \cdot \frac{x ^{3} - 9 x}{x ^{2} - 13 x + 30}

\frac{6}{x}

Solution steps

\frac{6 x - 60}{x ^{3} + 3 x ^{2}} \cdot \frac{x ^{3} - 9 x}{x ^{2} - 13 x + 30}

Cancel

\frac{x ^{3} - 9 x}{x ^{2} - 13 x + 30} : \frac{x ( x + 3 )}{x - 10}

= \frac{6 x - 60}{x ^{3} + 3 x ^{2}} \cdot \frac{x ( x + 3 )}{x - 10}

Apply the fraction rule:

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

= \frac{( 6 x - 60 ) x ( x + 3 )}{( x ^{3} + 3 x ^{2} ) ( x - 10 )}

Factor

6 x - 60 : 6 (x - 10)

= \frac{6 ( x - 10 ) x ( x + 3 )}{( x ^{3} + 3 x ^{2} ) ( x - 10 )}

Cancel the common factor:

x - 10

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

Factor

x^{3} + 3 x^{2} : x^{2} (x + 3)

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

Cancel the common factor:

x + 3

= \frac{6 x}{x ^{2}}

Apply exponent rule:

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

x^{2} = xx

= \frac{6 x}{xx}

Cancel the common factor:

x

= \frac{6}{x}

16 - 2 x

\frac{4 x ^{6} y ^{8}}{4 x y ^{7}}

\frac{5}{2} \times 2

(2 n^{4})^{4}

15 \times 12

What is (6x-60)/(x^3+3x^2)*(x^3-9x)/(x^2-13x+30) ?
The solution to (6x-60)/(x^3+3x^2)*(x^3-9x)/(x^2-13x+30) is 6/x