Solve [(2x+y/2x-y)-3(2x^2-xy)+y^2]div(-x)

$$[ ( 2 x + y / 2 x - y ) - 3 ( 2 x ^ { 2 } - x y ) + y ^ { 2 } ] \div ( - x )$$

Evaluate

$$-\frac{y^{2}}{x}-\frac{7y}{2}+6x+\frac{y}{x}-2$$

Short Solution Steps

Express \frac{y}{2}x as a single fraction.

$$\frac{2x+\frac{yx}{2}-y-3\left(2x^{2}-xy\right)+y^{2}}{-x}$$

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

$$\frac{\frac{2\left(2x-y\right)}{2}+\frac{yx}{2}-3\left(2x^{2}-xy\right)+y^{2}}{-x}$$

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

$$\frac{\frac{2\left(2x-y\right)+yx}{2}-3\left(2x^{2}-xy\right)+y^{2}}{-x}$$

Do the multiplications in 2\left(2x-y\right)+yx.

$$\frac{\frac{4x-2y+yx}{2}-3\left(2x^{2}-xy\right)+y^{2}}{-x}$$

Use the distributive property to multiply -3 by 2x^{2}-xy.

$$\frac{\frac{4x-2y+yx}{2}-6x^{2}+3xy+y^{2}}{-x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -6x^{2}+3xy+y^{2} times \frac{2}{2}.

$$\frac{\frac{4x-2y+yx}{2}+\frac{2\left(-6x^{2}+3xy+y^{2}\right)}{2}}{-x}$$

Since \frac{4x-2y+yx}{2} and \frac{2\left(-6x^{2}+3xy+y^{2}\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4x-2y+yx+2\left(-6x^{2}+3xy+y^{2}\right)}{2}}{-x}$$

Do the multiplications in 4x-2y+yx+2\left(-6x^{2}+3xy+y^{2}\right).

$$\frac{\frac{4x-2y+yx-12x^{2}+6xy+2y^{2}}{2}}{-x}$$

Combine like terms in 4x-2y+yx-12x^{2}+6xy+2y^{2}.

$$\frac{\frac{4x-2y+2y^{2}+7yx-12x^{2}}{2}}{-x}$$

Express \frac{\frac{4x-2y+2y^{2}+7yx-12x^{2}}{2}}{-x} as a single fraction.

$$\frac{4x-2y+2y^{2}+7yx-12x^{2}}{2\left(-x\right)}$$

Multiply 2 and -1 to get -2.

$$\frac{4x-2y+2y^{2}+7yx-12x^{2}}{-2x}$$

Expand

$$-\frac{y^{2}}{x}-\frac{7y}{2}+6x+\frac{y}{x}-2$$

Short Solution Steps

Express \frac{y}{2}x as a single fraction.

$$\frac{2x+\frac{yx}{2}-y-3\left(2x^{2}-xy\right)+y^{2}}{-x}$$

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

$$\frac{\frac{2\left(2x-y\right)}{2}+\frac{yx}{2}-3\left(2x^{2}-xy\right)+y^{2}}{-x}$$

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

$$\frac{\frac{2\left(2x-y\right)+yx}{2}-3\left(2x^{2}-xy\right)+y^{2}}{-x}$$

Do the multiplications in 2\left(2x-y\right)+yx.

$$\frac{\frac{4x-2y+yx}{2}-3\left(2x^{2}-xy\right)+y^{2}}{-x}$$

Use the distributive property to multiply -3 by 2x^{2}-xy.

$$\frac{\frac{4x-2y+yx}{2}-6x^{2}+3xy+y^{2}}{-x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -6x^{2}+3xy+y^{2} times \frac{2}{2}.

$$\frac{\frac{4x-2y+yx}{2}+\frac{2\left(-6x^{2}+3xy+y^{2}\right)}{2}}{-x}$$

Since \frac{4x-2y+yx}{2} and \frac{2\left(-6x^{2}+3xy+y^{2}\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4x-2y+yx+2\left(-6x^{2}+3xy+y^{2}\right)}{2}}{-x}$$

Do the multiplications in 4x-2y+yx+2\left(-6x^{2}+3xy+y^{2}\right).

$$\frac{\frac{4x-2y+yx-12x^{2}+6xy+2y^{2}}{2}}{-x}$$

Combine like terms in 4x-2y+yx-12x^{2}+6xy+2y^{2}.

$$\frac{\frac{4x-2y+2y^{2}+7yx-12x^{2}}{2}}{-x}$$

Express \frac{\frac{4x-2y+2y^{2}+7yx-12x^{2}}{2}}{-x} as a single fraction.

$$\frac{4x-2y+2y^{2}+7yx-12x^{2}}{2\left(-x\right)}$$

Multiply 2 and -1 to get -2.

$$\frac{4x-2y+2y^{2}+7yx-12x^{2}}{-2x}$$