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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

Cancel the common factor:

x + 1

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

(b - 6) (b - 5)

\frac{20}{40}

\frac{3}{2} \div \frac{1}{2}

(x - 2) (x - 2)

(x + 7) (x - 4)