Solve (x+2y)(x+3y)/(x^2-4y^2)(x^2-9y^2)

$$\frac { ( x + 2 y ) ( x + 3 y ) } { ( x ^ { 2 } - 4 y ^ { 2 } ) ( x ^ { 2 } - 9 y ^ { 2 } ) }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

$$\frac{1}{x^{2}-5xy+6y^{2}}$$

Expand

$$\frac{6}{\left(2x-4y\right)\left(3x-9y\right)}$$

Short Solution Steps

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

$$\frac{1}{x^{2}-5xy+6y^{2}}$$