Solve mx-my^2/2m+83m+12/my+mx/x-y

$$\frac{ \frac{ mx-m { y }^{ 2 } }{ 2m+8 } \frac{ 3m+12 }{ my+mx } }{ x-y }$$

Evaluate

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

Short Solution Steps

Multiply \frac{mx-my^{2}}{2m+8} times \frac{3m+12}{my+mx} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(mx-my^{2}\right)\left(3m+12\right)}{\left(2m+8\right)\left(my+mx\right)}}{x-y}$$

Express \frac{\frac{\left(mx-my^{2}\right)\left(3m+12\right)}{\left(2m+8\right)\left(my+mx\right)}}{x-y} as a single fraction.

$$\frac{\left(mx-my^{2}\right)\left(3m+12\right)}{\left(2m+8\right)\left(my+mx\right)\left(x-y\right)}$$

Factor the expressions that are not already factored.

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

Cancel out m\left(m+4\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{3x-3y^{2}}{2x^{2}-2y^{2}}$$

Expand

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

Short Solution Steps

Multiply \frac{mx-my^{2}}{2m+8} times \frac{3m+12}{my+mx} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(mx-my^{2}\right)\left(3m+12\right)}{\left(2m+8\right)\left(my+mx\right)}}{x-y}$$

Express \frac{\frac{\left(mx-my^{2}\right)\left(3m+12\right)}{\left(2m+8\right)\left(my+mx\right)}}{x-y} as a single fraction.

$$\frac{\left(mx-my^{2}\right)\left(3m+12\right)}{\left(2m+8\right)\left(my+mx\right)\left(x-y\right)}$$

Factor the expressions that are not already factored.

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

Cancel out m\left(m+4\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{3x-3y^{2}}{2x^{2}-2y^{2}}$$