What is (x^2+2x+1)/(x^4-1) ?

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

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simplify (x^2+2x+1)/(x^4-1)

simplify

\frac{x ^{2} + 2 x + 1}{x ^{4} - 1}

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

Solution steps

\frac{x ^{2} + 2 x + 1}{x ^{4} - 1}

Factor

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

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

Factor

x^{4} - 1 : (x^{2} + 1) (x + 1) (x - 1)

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

Cancel the common factor:

x + 1

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

2 \times 0

\frac{4}{3 x ^{2} + 15 x} + \frac{7 x}{x ^{2} + 10 x + 25}

- 6 x - 6 x

\frac{1 - \frac{1}{x ^{2}}}{3 + \frac{3}{x}}

(x - 7) (x + 9)

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