What is (2x+2y)/(x^2-2xy+y^2)*(x^2-xy)/(7y+7x) ?

The solution to (2x+2y)/(x^2-2xy+y^2)*(x^2-xy)/(7y+7x) is (2x)/(7(x-y))

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simplify (2x+2y)/(x^2-2xy+y^2)*(x^2-xy)/(7y+7x)

simplify

\frac{2 x + 2 y}{x ^{2} - 2 x y + y ^{2}} \cdot \frac{x ^{2} - x y}{7 y + 7 x}

\frac{2 x}{7 ( x - y )}

Solution steps

\frac{2 x + 2 y}{x ^{2} - 2 x y + y ^{2}} \cdot \frac{x ^{2} - x y}{7 y + 7 x}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{( 2 x + 2 y ) ( x ^{2} - x y )}{( x ^{2} - 2 x y + y ^{2} ) ( 7 y + 7 x )}

Factor out common term

2

= \frac{2 ( x + y ) ( x ^{2} - x y )}{( x ^{2} - 2 x y + y ^{2} ) ( 7 y + 7 x )}

Factor out common term

7

= \frac{2 ( x + y ) ( x ^{2} - x y )}{( x ^{2} - 2 x y + y ^{2} ) \cdot 7 ( y + x )}

Apply the commutative law:

y + x = x + y

= \frac{2 ( x + y ) ( x ^{2} - x y )}{( x ^{2} - 2 x y + y ^{2} ) \cdot 7 ( x + y )}

Cancel the common factor:

x + y

= \frac{2 ( x ^{2} - x y )}{( x ^{2} - 2 x y + y ^{2} ) \cdot 7}

Factor

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

= \frac{2 x ( x - y )}{( x ^{2} - 2 x y + y ^{2} ) \cdot 7}

Apply Perfect Square Formula:

a^{2} - 2 ab + b^{2} = (a - b)^{2}

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

= \frac{2 x ( x - y )}{( x - y ) ^{2} \cdot 7}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x - y)^{2} = (x - y) (x - y)

= \frac{2 x ( x - y )}{( x - y ) ( x - y ) \cdot 7}

Cancel the common factor:

x - y

= \frac{2 x}{( x - y ) \cdot 7}

= \frac{2 x}{7 ( x - y )}

x^{2} - 3 < 0

\frac{1}{4} + 2 x = - \frac{1}{2} - x

lo g_{4} (64) = y

8 - ∣ 4 x + 5 ∣ = 0

6 x^{2} + 8 x = 1

What is (2x+2y)/(x^2-2xy+y^2)*(x^2-xy)/(7y+7x) ?
The solution to (2x+2y)/(x^2-2xy+y^2)*(x^2-xy)/(7y+7x) is (2x)/(7(x-y))