Solve 2x/x^2-9y^2-2/x-3y

$$\frac{ 2x }{ { x }^{ 2 } -9 { y }^{ 2 } } - \frac{ 2 }{ x-3y }$$

Evaluate

$$-\frac{6y}{x^{2}-9y^{2}}$$

Short Solution Steps

Factor x^{2}-9y^{2}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3y\right)\left(x+3y\right) and x-3y is \left(x-3y\right)\left(x+3y\right). Multiply \frac{2}{x-3y} times \frac{x+3y}{x+3y}.

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

Since \frac{2x}{\left(x-3y\right)\left(x+3y\right)} and \frac{2\left(x+3y\right)}{\left(x-3y\right)\left(x+3y\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2x-2\left(x+3y\right).

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

Combine like terms in 2x-2x-6y.

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

Expand \left(x-3y\right)\left(x+3y\right).

$$\frac{-6y}{x^{2}-9y^{2}}$$

Factor

$$-\frac{6y}{x^{2}-9y^{2}}$$