What is factor (x+\frac{16)/(x+8)}{x-4/(x+8)} ?

The solution to factor (x+\frac{16)/(x+8)}{x-4/(x+8)} is ((x+4)^2)/(x(x+8)-4)

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factor (x+\frac{16)/(x+8)}{x-4/(x+8)}

factor

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

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

Solution steps

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

Join

x - \frac{4}{x + 8} : \frac{x ( x + 8 ) - 4}{x + 8}

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

Join

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

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

Divide fractions:

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

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

Cancel the common factor:

x + 8

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

\frac{5}{8} \cdot \frac{8}{9}

14 = 5 x^{2} - x - 4

0 = 3 (x - 4)^{2} - 5

1^{\frac{3}{2}}

x - 2 = 10 - 5 x

What is factor (x+\frac{16)/(x+8)}{x-4/(x+8)} ?
The solution to factor (x+\frac{16)/(x+8)}{x-4/(x+8)} is ((x+4)^2)/(x(x+8)-4)