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

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

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

simplify

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

\frac{x - 2 y}{y + 1}

Solution steps

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

Factor

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

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

Factor

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

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

Cancel the common factor:

x^{2} + 1

= \frac{x - 2 y}{y + 1}

e^{x l n (a)}

(5 x - 3) (7 x - 4)

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

4 \cdot 23

\frac{5}{13}

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