What is (x^3)/(4x-8)-4/(x^2+2x) ?

The solution to (x^3)/(4x-8)-4/(x^2+2x) is (x^5+2x^4-16x+32)/(4x(x-2)(x+2))

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simplify (x^3)/(4x-8)-4/(x^2+2x)

simplify

\frac{x ^{3}}{4 x - 8} - \frac{4}{x ^{2} + 2 x}

\frac{x ^{5} + 2 x ^{4} - 16 x + 32}{4 x ( x - 2 ) ( x + 2 )}

Solution steps

\frac{x ^{3}}{4 x - 8} - \frac{4}{x ^{2} + 2 x}

Least Common Multiplier of

4 x - 8, x^{2} + 2 x : 4 x (x - 2) (x + 2)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

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

Simplify

x^{4} (x + 2) - 16 (x - 2) : x^{5} + 2 x^{4} - 16 x + 32

= \frac{x ^{5} + 2 x ^{4} - 16 x + 32}{4 x ( x - 2 ) ( x + 2 )}

\frac{3}{7} + \frac{7}{8} + \frac{27}{28}

\frac{5 + i}{6 + 5 i}

\frac{16}{225}

4 n - 1 - 6 n + 8 - 8 n + 15

\frac{2}{1 + 2}

What is (x^3)/(4x-8)-4/(x^2+2x) ?
The solution to (x^3)/(4x-8)-4/(x^2+2x) is (x^5+2x^4-16x+32)/(4x(x-2)(x+2))