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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

x^{3} + 4 x^{2} : x^{2} (x + 4)

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

Apply exponent rule:

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

x^{2} = xx

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

Cancel the common factor:

x

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

\frac{8}{3} - 6

\frac{( 2 x ^{3} + 10 x ^{2} + 7 x - 15 )}{( x + 3 )}

cos^{2} (4 x) - sin^{2} (4 x)

(x + 1) \cdot (x + 3)

- 2 x^{2} + 2 x

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