What is (x^2+x)/(x^2+4x) ?

The solution to (x^2+x)/(x^2+4x) is (x+1)/(x+4)

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simplify (x^2+x)/(x^2+4x)

simplify

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

\frac{x + 1}{x + 4}

Solution steps

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

Factor

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

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

Factor

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

= \frac{x ( x + 1 )}{x ( x + 4 )}

Cancel the common factor:

x

= \frac{x + 1}{x + 4}