What is (x^2+x)/(x^2+2x+1) ?

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

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simplify (x^2+x)/(x^2+2x+1)

simplify

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

\frac{x}{x + 1}

Solution steps

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

Factor

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

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

Factor

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

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

Apply exponent rule:

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

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

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

Cancel the common factor:

x + 1

= \frac{x}{x + 1}

\frac{x ^{2} - 36}{x + 6}

13 0^{2}

\frac{4 x - 8}{x - 3} \cdot \frac{x ^{2} - 81}{x ^{2} - 11 x + 18}

\frac{1 2 ^{2} 3}{4}

- \frac{1}{2} \cdot (- 3)