What is expand (x-y)/(2x-2y)+(x^2-y^2)/(6x-6y) ?

The solution to expand (x-y)/(2x-2y)+(x^2-y^2)/(6x-6y) is 1/2+x/6+y/6

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expand (x-y)/(2x-2y)+(x^2-y^2)/(6x-6y)

expand

\frac{x - y}{2 x - 2 y} + \frac{x ^{2} - y ^{2}}{6 x - 6 y}

\frac{1}{2} + \frac{x}{6} + \frac{y}{6}

Solution steps

\frac{x - y}{2 x - 2 y} + \frac{x ^{2} - y ^{2}}{6 x - 6 y}

Cancel

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

= \frac{1}{2} + \frac{x ^{2} - y ^{2}}{6 x - 6 y}

Cancel

\frac{x ^{2} - y ^{2}}{6 x - 6 y} : \frac{x + y}{6}

= \frac{1}{2} + \frac{x + y}{6}

Apply the fraction rule:

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

\frac{x + y}{6} = \frac{x}{6} + \frac{y}{6}

= \frac{1}{2} + \frac{x}{6} + \frac{y}{6}

\frac{2 y ^{3} ( y - 1 )}{( 2 y - 1 )}

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

π (3 r + 8 s)^{2} \cdot (12 r + 32 s)

(f \circ g) 3 (- x + 7) - 2

, (s + 1) (\frac{s}{2} + 1) (\frac{s}{3} + 1)

What is expand (x-y)/(2x-2y)+(x^2-y^2)/(6x-6y) ?
The solution to expand (x-y)/(2x-2y)+(x^2-y^2)/(6x-6y) is 1/2+x/6+y/6