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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

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}

- (x + 1)^{2}

(x - 3) 2

\frac{8}{18}

\frac{2}{3} \div \frac{4}{5}

(4 d^{2} - 2 d^{7})^{2}