What is (3x^5)/(3x^4+6x^3-3x^2-6x) ?

The solution to (3x^5)/(3x^4+6x^3-3x^2-6x) is (x^4)/((x+2)(x+1)(x-1))

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simplify (3x^5)/(3x^4+6x^3-3x^2-6x)

simplify

\frac{3 x ^{5}}{3 x ^{4} + 6 x ^{3} - 3 x ^{2} - 6 x}

\frac{x ^{4}}{( x + 2 ) ( x + 1 ) ( x - 1 )}

Solution steps

\frac{3 x ^{5}}{3 x ^{4} + 6 x ^{3} - 3 x ^{2} - 6 x}

Factor

3 x^{4} + 6 x^{3} - 3 x^{2} - 6 x : 3 x (x^{3} + 2 x^{2} - x - 2)

= \frac{3 x ^{5}}{3 x ( x ^{3} + 2 x ^{2} - x - 2 )}

= \frac{3 x ^{5}}{3 x ( ( x ^{3} + 2 x ^{2} ) + ( - x - 2 ) )}

Factor out

x^{2}

from

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

Factor out

- 1

from

- x - 2 : - (x + 2)

= \frac{3 x ^{5}}{3 x ( x ^{2} ( x + 2 ) - ( x + 2 ) )}

Factor out common term

(x + 2) : (x + 2) (x^{2} - 1)

= \frac{3 x ^{5}}{3 x ( x + 2 ) ( x ^{2} - 1 )}

Factor

x^{2} - 1 : (x + 1) (x - 1)

= \frac{3 x ^{5}}{3 x ( x + 2 ) ( x + 1 ) ( x - 1 )}

Cancel the common factor:

3

= \frac{x ^{5}}{x ( x + 2 ) ( x + 1 ) ( x - 1 )}

Apply exponent rule:

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

x^{5} = x x^{4}

= \frac{x x ^{4}}{x ( x + 2 ) ( x + 1 ) ( x - 1 )}

Cancel the common factor:

x

= \frac{x ^{4}}{( x + 2 ) ( x + 1 ) ( x - 1 )}

\frac{\frac{32 x ^{3} y}{y ^{8}}}{\frac{y ^{7}}{8 x ^{4}}}

\frac{1}{4} - \frac{3}{2} + \frac{9}{2}

\frac{cosh ^{2} ( x )}{1 + sinh ^{2} ( x )}

\frac{x ^{2} - 6 x - 16}{x ^{2} - 5 x - 14}

\frac{144}{360}

What is (3x^5)/(3x^4+6x^3-3x^2-6x) ?
The solution to (3x^5)/(3x^4+6x^3-3x^2-6x) is (x^4)/((x+2)(x+1)(x-1))