What is (x^2-64)/(7x)*(3x^3)/(x^2+x-72) ?

The solution to (x^2-64)/(7x)*(3x^3)/(x^2+x-72) is (3x^2(x+8))/(7(x+9))

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simplify (x^2-64)/(7x)*(3x^3)/(x^2+x-72)

simplify

\frac{x ^{2} - 64}{7 x} \cdot \frac{3 x ^{3}}{x ^{2} + x - 72}

\frac{3 x ^{2} ( x + 8 )}{7 ( x + 9 )}

Solution steps

\frac{x ^{2} - 64}{7 x} \cdot \frac{3 x ^{3}}{x ^{2} + x - 72}

Apply the fraction rule:

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

= \frac{( x ^{2} - 64 ) \cdot 3 x ^{3}}{7 x ( x ^{2} + x - 72 )}

Apply exponent rule:

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

x^{3} = x x^{2}

= \frac{( x ^{2} - 64 ) \cdot 3 x x ^{2}}{7 x ( x ^{2} + x - 72 )}

Cancel the common factor:

x

= \frac{( x ^{2} - 64 ) \cdot 3 x ^{2}}{7 ( x ^{2} + x - 72 )}

Factor

x^{2} - 64 : (x + 8) (x - 8)

= \frac{( x + 8 ) ( x - 8 ) \cdot 3 x ^{2}}{7 ( x ^{2} + x - 72 )}

Factor

x^{2} + x - 72 : (x - 8) (x + 9)

= \frac{( x + 8 ) ( x - 8 ) \cdot 3 x ^{2}}{7 ( x - 8 ) ( x + 9 )}

Cancel the common factor:

x - 8

= \frac{( x + 8 ) \cdot 3 x ^{2}}{7 ( x + 9 )}

= \frac{3 ( x + 8 ) x ^{2}}{7 ( x + 9 )}

= \frac{3 x ^{2} ( x + 8 )}{7 ( x + 9 )}

\frac{28}{15}

(x + 5) (2 x^{2} + 2 x - 3)

\frac{54}{7}

(3 + 5 i) (2 - 7 i^{4})

4 lo g_{2} (2)

What is (x^2-64)/(7x)*(3x^3)/(x^2+x-72) ?
The solution to (x^2-64)/(7x)*(3x^3)/(x^2+x-72) is (3x^2(x+8))/(7(x+9))