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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

x - y, x^{3} - y^{3} : (x - y) (x^{3} - y^{3})

Adjust Fractions based on the LCM

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

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

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

Simplify

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

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

Cancel

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

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

2^{x} + 2^{x}

\frac{e ^{- 2} \cdot 2 ^{2}}{2 !}

x^{2} - 8 x + 16

\frac{x ^{2} - 25}{x ^{2} - 6 x + 5}

(5)^{5}

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