Solve (y-2x)(3x-2y)/(y-3x)(2x-y)div(6x^2-13xy+6y^2)

$$\frac{ (y-2x)(3x-2y) }{ (y-3x)(2x-y) } \div (6 { x }^{ 2 } -13xy+6 { y }^{ 2 } )$$

Evaluate

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

Short Solution Steps

Express \frac{\frac{\left(y-2x\right)\left(3x-2y\right)}{\left(y-3x\right)\left(2x-y\right)}}{6x^{2}-13xy+6y^{2}} as a single fraction.

$$\frac{\left(y-2x\right)\left(3x-2y\right)}{\left(y-3x\right)\left(2x-y\right)\left(6x^{2}-13xy+6y^{2}\right)}$$

Extract the negative sign in y-2x.

$$\frac{-\left(3x-2y\right)\left(2x-y\right)}{\left(-3x+y\right)\left(2x-y\right)\left(6x^{2}-13xy+6y^{2}\right)}$$

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

$$\frac{-\left(3x-2y\right)}{\left(-3x+y\right)\left(6x^{2}-13xy+6y^{2}\right)}$$

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

$$\frac{-1}{-6x^{2}+11xy-3y^{2}}$$

Expand

$$-\frac{3}{\left(y-3x\right)\left(6x-9y\right)}$$

Short Solution Steps

Express \frac{\frac{\left(y-2x\right)\left(3x-2y\right)}{\left(y-3x\right)\left(2x-y\right)}}{6x^{2}-13xy+6y^{2}} as a single fraction.

$$\frac{\left(y-2x\right)\left(3x-2y\right)}{\left(y-3x\right)\left(2x-y\right)\left(6x^{2}-13xy+6y^{2}\right)}$$

Extract the negative sign in y-2x.

$$\frac{-\left(3x-2y\right)\left(2x-y\right)}{\left(-3x+y\right)\left(2x-y\right)\left(6x^{2}-13xy+6y^{2}\right)}$$

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

$$\frac{-\left(3x-2y\right)}{\left(-3x+y\right)\left(6x^{2}-13xy+6y^{2}\right)}$$

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

$$\frac{-1}{-6x^{2}+11xy-3y^{2}}$$