Solve 3/x-y+4/x=

$$\frac { 3 } { x - y } + \frac { 4 } { x } =$$

Evaluate

$$\frac{7x-4y}{x\left(x-y\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-y and x is x\left(x-y\right). Multiply \frac{3}{x-y} times \frac{x}{x}. Multiply \frac{4}{x} times \frac{x-y}{x-y}.

$$\frac{3x}{x\left(x-y\right)}+\frac{4\left(x-y\right)}{x\left(x-y\right)}$$

Since \frac{3x}{x\left(x-y\right)} and \frac{4\left(x-y\right)}{x\left(x-y\right)} have the same denominator, add them by adding their numerators.

$$\frac{3x+4\left(x-y\right)}{x\left(x-y\right)}$$

Do the multiplications in 3x+4\left(x-y\right).

$$\frac{3x+4x-4y}{x\left(x-y\right)}$$

Combine like terms in 3x+4x-4y.

$$\frac{7x-4y}{x\left(x-y\right)}$$

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

$$\frac{7x-4y}{x^{2}-xy}$$

Differentiate w.r.t. x

$$\frac{-7x^{2}+8xy-4y^{2}}{\left(x\left(x-y\right)\right)^{2}}$$