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

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

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

simplify

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

3 x - 2 y

Solution steps

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

Factor

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

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

Apply the commutative law:

y + 2 x = 2 x + y

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

Cancel the common factor:

2 x + y

= 3 x - 2 y

\frac{4 ^{2} 3}{4}

\frac{5 - x}{x - 5}

- 3 - 10

- 3 x + x

- 6 - 12