What is expand (2x+2y-6)/(3(x^2+2xy+4y^2-6x-12y)^{2/3)} ?

The solution to expand (2x+2y-6)/(3(x^2+2xy+4y^2-6x-12y)^{2/3)} is

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expand (2x+2y-6)/(3(x^2+2xy+4y^2-6x-12y)^{2/3)}

expand

\frac{2 x + 2 y - 6}{3 ( x ^{2} + 2 x y + 4 y ^{2} - 6 x - 12 y ) ^{\frac{2}{3}}}

\frac{2 x}{3 ( x ^{2} + 2 x y + 4 y ^{2} - 6 x - 12 y ) ^{\frac{2}{3}}} + \frac{2 y}{3 ( x ^{2} + 2 x y + 4 y ^{2} - 6 x - 12 y ) ^{\frac{2}{3}}} - \frac{2}{( x ^{2} + 2 x y + 4 y ^{2} - 6 x - 12 y ) ^{\frac{2}{3}}}

Solution steps

\frac{2 x + 2 y - 6}{3 ( x ^{2} + 2 x y + 4 y ^{2} - 6 x - 12 y ) ^{\frac{2}{3}}}

Apply the fraction rule:

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

\frac{2 x + 2 y - 6}{3 ( x ^{2} + 2 x y + 4 y ^{2} - 6 x - 12 y ) ^{\frac{2}{3}}} = \frac{2 x}{3 ( x ^{2} + 2 x y + 4 y ^{2} - 6 x - 12 y ) ^{\frac{2}{3}}} + \frac{2 y}{3 ( x ^{2} + 2 x y + 4 y ^{2} - 6 x - 12 y ) ^{\frac{2}{3}}} - \frac{6}{3 ( x ^{2} + 2 x y + 4 y ^{2} - 6 x - 12 y ) ^{\frac{2}{3}}}

= \frac{2 x}{3 ( x ^{2} + 2 x y - 6 x + 4 y ^{2} - 12 y ) ^{\frac{2}{3}}} + \frac{2 y}{3 ( x ^{2} + 2 x y - 6 x + 4 y ^{2} - 12 y ) ^{\frac{2}{3}}} - \frac{6}{3 ( x ^{2} + 2 x y - 6 x + 4 y ^{2} - 12 y ) ^{\frac{2}{3}}}

Divide the numbers:

\frac{6}{3} = 2

= \frac{2 x}{3 ( x ^{2} + 2 x y - 6 x + 4 y ^{2} - 12 y ) ^{\frac{2}{3}}} + \frac{2 y}{3 ( x ^{2} + 2 x y - 6 x + 4 y ^{2} - 12 y ) ^{\frac{2}{3}}} - \frac{2}{( x ^{2} + 2 x y - 6 x + 4 y ^{2} - 12 y ) ^{\frac{2}{3}}}

\frac{1}{( 1 + x ) ^{5}}

a (1 - e^{- \frac{x}{b}})

(x^{2} + x - 2) (4 x^{3} - 2 x^{2} + 7 x - 11)^{'}

\frac{2}{2 - i}

\frac{1}{( x + 6 x ) ^{4}}

What is expand (2x+2y-6)/(3(x^2+2xy+4y^2-6x-12y)^{2/3)} ?
The solution to expand (2x+2y-6)/(3(x^2+2xy+4y^2-6x-12y)^{2/3)} is