Solve 2(3x-y)+(xy-4y^2)div(-y)

$$2 ( 3 x - y ) + ( x y - 4 y ^ { 2 } ) \div ( - y )$$

Evaluate

$$5x+2y$$

Short Solution Steps

Use the distributive property to multiply 2 by 3x-y.

$$6x-2y+\frac{xy-4y^{2}}{-y}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x-2y times \frac{-y}{-y}.

$$\frac{\left(6x-2y\right)\left(-1\right)y}{-y}+\frac{xy-4y^{2}}{-y}$$

Since \frac{\left(6x-2y\right)\left(-1\right)y}{-y} and \frac{xy-4y^{2}}{-y} have the same denominator, add them by adding their numerators.

$$\frac{\left(6x-2y\right)\left(-1\right)y+xy-4y^{2}}{-y}$$

Do the multiplications in \left(6x-2y\right)\left(-1\right)y+xy-4y^{2}.

$$\frac{-6xy+2y^{2}+xy-4y^{2}}{-y}$$

Combine like terms in -6xy+2y^{2}+xy-4y^{2}.

$$\frac{-2y^{2}-5xy}{-y}$$

Factor the expressions that are not already factored in \frac{-2y^{2}-5xy}{-y}.

$$\frac{y\left(-5x-2y\right)}{-y}$$

Cancel out y in both numerator and denominator.

$$\frac{-5x-2y}{-1}$$

Expand

$$5x+2y$$

Short Solution Steps

Use the distributive property to multiply 2 by 3x-y.

$$6x-2y+\frac{xy-4y^{2}}{-y}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x-2y times \frac{-y}{-y}.

$$\frac{\left(6x-2y\right)\left(-1\right)y}{-y}+\frac{xy-4y^{2}}{-y}$$

Since \frac{\left(6x-2y\right)\left(-1\right)y}{-y} and \frac{xy-4y^{2}}{-y} have the same denominator, add them by adding their numerators.

$$\frac{\left(6x-2y\right)\left(-1\right)y+xy-4y^{2}}{-y}$$

Do the multiplications in \left(6x-2y\right)\left(-1\right)y+xy-4y^{2}.

$$\frac{-6xy+2y^{2}+xy-4y^{2}}{-y}$$

Combine like terms in -6xy+2y^{2}+xy-4y^{2}.

$$\frac{-2y^{2}-5xy}{-y}$$

Factor the expressions that are not already factored in \frac{-2y^{2}-5xy}{-y}.

$$\frac{y\left(-5x-2y\right)}{-y}$$

Cancel out y in both numerator and denominator.

$$\frac{-5x-2y}{-1}$$