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

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

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

simplify

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

x - 2

Solution steps

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

Factor

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

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

Factor

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

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

Cancel the common factor:

x

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

Cancel the common factor:

x + 3

= x - 2

- 4 \times \frac{1}{3}

3 6^{\frac{1}{6}}

\frac{4 + i}{2 + 9 i}

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

\frac{7 - 6 i}{7 + i}