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}

9 a^{3} \cdot x^{2} - 18 a \cdot x^{3}

\frac{1 + ( tan ( x ) )}{( cos ( x ) )}

b^{10} - 6 + 5 - 3 - 2 + 1

\frac{c [ ( - 77 ) + 5 ]}{[ ( - 3 ) + 6 ]}

8 x^{3} + 216 y^{3}

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)