Solve 8x^2/2x-3y+18y^2/3y-2x

$$\frac { 8 x ^ { 2 } } { 2 x - 3 y } + \frac { 18 y ^ { 2 } } { 3 y - 2 x }$$

Evaluate

$$4x+6y$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x-3y and 3y-2x is -2x+3y. Multiply \frac{8x^{2}}{2x-3y} times \frac{-1}{-1}.

$$\frac{-8x^{2}}{-2x+3y}+\frac{18y^{2}}{-2x+3y}$$

Since \frac{-8x^{2}}{-2x+3y} and \frac{18y^{2}}{-2x+3y} have the same denominator, add them by adding their numerators.

$$\frac{-8x^{2}+18y^{2}}{-2x+3y}$$

Factor the expressions that are not already factored in \frac{-8x^{2}+18y^{2}}{-2x+3y}.

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

Extract the negative sign in 2x-3y.

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

Cancel out -2x+3y in both numerator and denominator.

$$-2\left(-2x-3y\right)$$

Expand the expression.

$$4x+6y$$

Factor

$$2\left(2x+3y\right)$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x-3y and 3y-2x is -2x+3y. Multiply \frac{8x^{2}}{2x-3y} times \frac{-1}{-1}.

$$factor(\frac{-8x^{2}}{-2x+3y}+\frac{18y^{2}}{-2x+3y})$$

Since \frac{-8x^{2}}{-2x+3y} and \frac{18y^{2}}{-2x+3y} have the same denominator, add them by adding their numerators.

$$factor(\frac{-8x^{2}+18y^{2}}{-2x+3y})$$

Factor the expressions that are not already factored in \frac{-8x^{2}+18y^{2}}{-2x+3y}.

$$factor(\frac{2\left(-2x-3y\right)\left(2x-3y\right)}{-2x+3y})$$

Extract the negative sign in 2x-3y.

$$factor(\frac{-2\left(-2x-3y\right)\left(-2x+3y\right)}{-2x+3y})$$

Cancel out -2x+3y in both numerator and denominator.

$$factor(-2\left(-2x-3y\right))$$

Expand the expression.

$$factor(4x+6y)$$

Factor out 2.

$$2\left(2x+3y\right)$$