What is (x^3-2x^2+x-2)/(x^2-4) ?

The solution to (x^3-2x^2+x-2)/(x^2-4) is (x^2+1)/(x+2)

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simplify (x^3-2x^2+x-2)/(x^2-4)

simplify

\frac{x ^{3} - 2 x ^{2} + x - 2}{x ^{2} - 4}

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

Solution steps

\frac{x ^{3} - 2 x ^{2} + x - 2}{x ^{2} - 4}

Factor

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

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

Factor

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

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

Cancel the common factor:

x - 2

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

(- y + 4) (2 y - 1)

\frac{i ^{5235} ( 2 - i ) ^{4}}{( 7 i - ( 4 + 3 i ) - 2 ) ^{3}}

\frac{9 m}{5 m ^{2}} \cdot \frac{7}{2}

\frac{2 5 - 3}{5 + 1}

\frac{5 3 + 2}{3 - 1}

What is (x^3-2x^2+x-2)/(x^2-4) ?
The solution to (x^3-2x^2+x-2)/(x^2-4) is (x^2+1)/(x+2)