Solve y/x-y+6-x/y-x

$$\frac { y } { x - y } + 6 - \frac { x } { y - x }$$

Evaluate

$$\frac{7x-5y}{x-y}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{x-y}{x-y}.

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

Since \frac{y}{x-y} and \frac{6\left(x-y\right)}{x-y} have the same denominator, add them by adding their numerators.

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

Do the multiplications in y+6\left(x-y\right).

$$\frac{y+6x-6y}{x-y}-\frac{x}{y-x}$$

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

$$\frac{-5y+6x}{x-y}-\frac{x}{y-x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-y and y-x is x-y. Multiply \frac{x}{y-x} times \frac{-1}{-1}.

$$\frac{-5y+6x}{x-y}-\frac{-x}{x-y}$$

Since \frac{-5y+6x}{x-y} and \frac{-x}{x-y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5y+6x-\left(-x\right)}{x-y}$$

Do the multiplications in -5y+6x-\left(-x\right).

$$\frac{-5y+6x+x}{x-y}$$

Combine like terms in -5y+6x+x.

$$\frac{-5y+7x}{x-y}$$

Differentiate w.r.t. x

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