What is ((x^2+4x)/8)/((x^2-16)/4) ?

The solution to ((x^2+4x)/8)/((x^2-16)/4) is x/(2(x-4))

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simplify ((x^2+4x)/8)/((x^2-16)/4)

simplify

\frac{\frac{x ^{2} + 4 x}{8}}{\frac{x ^{2} - 16}{4}}

\frac{x}{2 ( x - 4 )}

Solution steps

\frac{\frac{x ^{2} + 4 x}{8}}{\frac{x ^{2} - 16}{4}}

Apply the fraction rule:

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

= \frac{( x ^{2} + 4 x ) \cdot 4}{8 ( x ^{2} - 16 )}

Cancel

\frac{( x ^{2} + 4 x ) \cdot 4}{8 ( x ^{2} - 16 )} : \frac{x}{2 ( x - 4 )}

= \frac{x}{2 ( x - 4 )}

- 3^{2} + 4^{2}

1. 2^{4}

- 4 \cdot (- \frac{1}{4})

\frac{a ^{2} - b ^{2}}{a ^{3} - b ^{3}}

(x + 4) (2 x - 1)

What is ((x^2+4x)/8)/((x^2-16)/4) ?
The solution to ((x^2+4x)/8)/((x^2-16)/4) is x/(2(x-4))