What is (x^2-1)/(x^3+3x^2-x-3) ?

The solution to (x^2-1)/(x^3+3x^2-x-3) is 1/(x+3)

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simplify (x^2-1)/(x^3+3x^2-x-3)

simplify

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

\frac{1}{x + 3}

Solution steps

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

Factor

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

= \frac{( x + 1 ) ( x - 1 )}{x ^{3} + 3 x ^{2} - x - 3}

Factor

x^{3} + 3 x^{2} - x - 3 : (x + 3) (x + 1) (x - 1)

= \frac{( x + 1 ) ( x - 1 )}{( x + 3 ) ( x + 1 ) ( x - 1 )}

Cancel the common factor:

x + 1

= \frac{x - 1}{( x + 3 ) ( x - 1 )}

Cancel the common factor:

x - 1

= \frac{1}{x + 3}

- 32 \cdot \frac{1}{243}

169 - 144 \cdot 16 + 9

\frac{1}{2} + \frac{3}{4} - \frac{17}{4}

2^{m} 2^{2 n}

2 y (y^{2} - 5 y - 3) + y (y + 1)

What is (x^2-1)/(x^3+3x^2-x-3) ?
The solution to (x^2-1)/(x^3+3x^2-x-3) is 1/(x+3)