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

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

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

simplify

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

\frac{x + 2}{x}

Solution steps

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

Factor

x^{4} + x^{3} - 2 x^{2} : x^{2} (x - 1) (x + 2)

= \frac{x ^{2} ( x - 1 ) ( x + 2 )}{x ^{4} - x ^{3}}

Factor

x^{4} - x^{3} : x^{3} (x - 1)

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

Cancel the common factor:

x - 1

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

x^{3} = x^{2} x

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

Cancel the common factor:

x^{2}

= \frac{x + 2}{x}

g^{3} + 8

(8^{2})^{4}

7 x^{3} + 4 x

2 x^{2} - 16 x + 24

2^{5 x}

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