What is (v^3+11v^2+18v)/(v^2+v-2) ?

The solution to (v^3+11v^2+18v)/(v^2+v-2) is (v(v+9))/(v-1)

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simplify (v^3+11v^2+18v)/(v^2+v-2)

simplify

\frac{v ^{3} + 11 v ^{2} + 18 v}{v ^{2} + v - 2}

\frac{v ( v + 9 )}{v - 1}

Solution steps

\frac{v ^{3} + 11 v ^{2} + 18 v}{v ^{2} + v - 2}

Factor

v^{3} + 11 v^{2} + 18 v : v (v + 2) (v + 9)

= \frac{v ( v + 2 ) ( v + 9 )}{v ^{2} + v - 2}

Factor

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

= \frac{v ( v + 2 ) ( v + 9 )}{( v - 1 ) ( v + 2 )}

Cancel the common factor:

v + 2

= \frac{v ( v + 9 )}{v - 1}

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

\frac{2 x + 1}{x + 1} + \frac{x - 1}{x ^{2} - 1}

\frac{5 x ^{2} - 10 x}{5 x}

x^{4} + 6 x^{2} + 8

4 (\frac{y}{2} - 2) - (8 + y)

What is (v^3+11v^2+18v)/(v^2+v-2) ?
The solution to (v^3+11v^2+18v)/(v^2+v-2) is (v(v+9))/(v-1)