Solve 2/x-y+4/y-x+2/x-y

$$\frac { 2 } { x - y } + \frac { 4 } { y - x } + \frac { 2 } { x - y }$$

Evaluate

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Short Solution Steps

Combine \frac{2}{x-y} and \frac{2}{x-y} to get 2\times \frac{2}{x-y}.

$$2\times \frac{2}{x-y}+\frac{4}{y-x}$$

Express 2\times \frac{2}{x-y} as a single fraction.

$$\frac{2\times 2}{x-y}+\frac{4}{y-x}$$

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{2\times 2}{x-y} times \frac{-1}{-1}.

$$\frac{-2\times 2}{-x+y}+\frac{4}{-x+y}$$

Since \frac{-2\times 2}{-x+y} and \frac{4}{-x+y} have the same denominator, add them by adding their numerators.

$$\frac{-2\times 2+4}{-x+y}$$

Do the multiplications in -2\times 2+4.

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

Do the calculations in -4+4.

$$\frac{0}{-x+y}$$

Zero divided by any non-zero term gives zero.

$$0$$

Factor

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