Solve 5y-5x/3y-2x:x^2-y^2/4x^2-9y^2=

$$\frac { 5 y - 5 x } { 3 y - 2 x } : \frac { x ^ { 2 } - y ^ { 2 } } { 4 x ^ { 2 } - 9 y ^ { 2 } } =$$

Evaluate

$$\frac{5\left(2x+3y\right)}{x+y}$$

Short Solution Steps

Divide \frac{5y-5x}{3y-2x} by \frac{x^{2}-y^{2}}{4x^{2}-9y^{2}} by multiplying \frac{5y-5x}{3y-2x} by the reciprocal of \frac{x^{2}-y^{2}}{4x^{2}-9y^{2}}.

$$\frac{\left(5y-5x\right)\left(4x^{2}-9y^{2}\right)}{\left(3y-2x\right)\left(x^{2}-y^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{5\left(-x+y\right)\left(2x-3y\right)\left(2x+3y\right)}{\left(x+y\right)\left(x-y\right)\left(-2x+3y\right)}$$

Extract the negative sign in 2x-3y. Extract the negative sign in y-x.

$$\frac{-\left(-1\right)\times 5\left(x-y\right)\left(-2x+3y\right)\left(2x+3y\right)}{\left(x+y\right)\left(x-y\right)\left(-2x+3y\right)}$$

Cancel out \left(x-y\right)\left(-2x+3y\right) in both numerator and denominator.

$$\frac{-\left(-1\right)\times 5\left(2x+3y\right)}{x+y}$$

Expand the expression.

$$\frac{10x+15y}{x+y}$$

Expand

$$\frac{5\left(2x+3y\right)}{x+y}$$

Short Solution Steps

Divide \frac{5y-5x}{3y-2x} by \frac{x^{2}-y^{2}}{4x^{2}-9y^{2}} by multiplying \frac{5y-5x}{3y-2x} by the reciprocal of \frac{x^{2}-y^{2}}{4x^{2}-9y^{2}}.

$$\frac{\left(5y-5x\right)\left(4x^{2}-9y^{2}\right)}{\left(3y-2x\right)\left(x^{2}-y^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{5\left(-x+y\right)\left(2x-3y\right)\left(2x+3y\right)}{\left(x+y\right)\left(x-y\right)\left(-2x+3y\right)}$$

Extract the negative sign in 2x-3y. Extract the negative sign in y-x.

$$\frac{-\left(-1\right)\times 5\left(x-y\right)\left(-2x+3y\right)\left(2x+3y\right)}{\left(x+y\right)\left(x-y\right)\left(-2x+3y\right)}$$

Cancel out \left(x-y\right)\left(-2x+3y\right) in both numerator and denominator.

$$\frac{-\left(-1\right)\times 5\left(2x+3y\right)}{x+y}$$

Expand the expression.

$$\frac{10x+15y}{x+y}$$