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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

x - y, x^{2} - y^{2} : (x - y) (x^{2} - y^{2})

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

Cancel

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

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

\frac{3}{5} - \frac{3}{4}

8 x + 1 \geq - 71

y, 4 x^{2} + y^{2} - 8 x = - 4

(1 + i)^{3}

\frac{- 15 r ^{6} s ^{7} t ^{4}}{3 r ^{2} s ^{9} t ^{7}}

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