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

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

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

simplify

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

\frac{x}{x - 2}

Solution steps

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

Factor

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

= \frac{x ( x + 3 )}{x ^{2} + x - 6}

Factor

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

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

Cancel the common factor:

x + 3

= \frac{x}{x - 2}

\frac{a ^{2} - 1}{a ^{2} - a}

3 \div \frac{1}{6}

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

12 x^{3} - 12 x^{2}

\frac{x ^{2} + 8 x + 16}{x ^{2} + 3 x - 4}