What is (2x)/(2x+y)*(2xy+x^2)/(6x^2) ?

The solution to (2x)/(2x+y)*(2xy+x^2)/(6x^2) is (2y+x)/(3(2x+y))

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simplify (2x)/(2x+y)*(2xy+x^2)/(6x^2)

simplify

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

\frac{2 y + x}{3 ( 2 x + y )}

Solution steps

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

Cancel

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

= \frac{2 x}{2 x + y} \cdot \frac{2 y + x}{6 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 ) \cdot 6 x}

Cancel the common factor:

x

= \frac{2 ( 2 y + x )}{( 2 x + y ) \cdot 6}

Factor the number:

6 = 2 \cdot 3

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

Cancel the common factor:

2

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

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

5 + \frac{x}{4} = \frac{1}{3} (2 - \frac{x}{2}) - \frac{2}{3} + \frac{1}{4} (10 - \frac{5 x}{3})

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

(t - \frac{1}{2})^{2} = - \frac{73}{4}

3.66 = (\frac{7281}{( 1000 ) + 7281}) (x)

45.3 \cdot \frac{1}{26.928}

What is (2x)/(2x+y)*(2xy+x^2)/(6x^2) ?
The solution to (2x)/(2x+y)*(2xy+x^2)/(6x^2) is (2y+x)/(3(2x+y))