Solve 4x^2-10/x-3y*9y^2-x^2/6x^2-15

$$\frac { 4 x ^ { 2 } - 10 } { x - 3 y } \times \frac { 9 y ^ { 2 } - x ^ { 2 } } { 6 x ^ { 2 } - 15 }$$

Evaluate

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

Short Solution Steps

Multiply \frac{4x^{2}-10}{x-3y} times \frac{9y^{2}-x^{2}}{6x^{2}-15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4x^{2}-10\right)\left(9y^{2}-x^{2}\right)}{\left(x-3y\right)\left(6x^{2}-15\right)}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in 3y-x.

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

Cancel out \left(x-3y\right)\left(2x^{2}-5\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{-2x-6y}{3}$$

Expand

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

Short Solution Steps

Multiply \frac{4x^{2}-10}{x-3y} times \frac{9y^{2}-x^{2}}{6x^{2}-15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4x^{2}-10\right)\left(9y^{2}-x^{2}\right)}{\left(x-3y\right)\left(6x^{2}-15\right)}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in 3y-x.

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

Cancel out \left(x-3y\right)\left(2x^{2}-5\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{-2x-6y}{3}$$