Solve 1-1/y+1/x/frac{1{x}-1/y}

$$1- \frac{ \frac{ 1 }{ y } + \frac{ 1 }{ x } }{ \frac{ 1 }{ x } - \frac{ 1 }{ y } }$$

Evaluate

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

Short Solution Steps

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

$$1-\frac{\frac{x}{xy}+\frac{y}{xy}}{\frac{1}{x}-\frac{1}{y}}$$

Since \frac{x}{xy} and \frac{y}{xy} have the same denominator, add them by adding their numerators.

$$1-\frac{\frac{x+y}{xy}}{\frac{1}{x}-\frac{1}{y}}$$

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

$$1-\frac{\frac{x+y}{xy}}{\frac{y}{xy}-\frac{x}{xy}}$$

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

$$1-\frac{\frac{x+y}{xy}}{\frac{y-x}{xy}}$$

Divide \frac{x+y}{xy} by \frac{y-x}{xy} by multiplying \frac{x+y}{xy} by the reciprocal of \frac{y-x}{xy}.

$$1-\frac{\left(x+y\right)xy}{xy\left(y-x\right)}$$

Cancel out xy in both numerator and denominator.

$$1-\frac{x+y}{-x+y}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{-x+y}{-x+y}.

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

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

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

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

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

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

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

Expand

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

Short Solution Steps

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

$$1-\frac{\frac{x}{xy}+\frac{y}{xy}}{\frac{1}{x}-\frac{1}{y}}$$

Since \frac{x}{xy} and \frac{y}{xy} have the same denominator, add them by adding their numerators.

$$1-\frac{\frac{x+y}{xy}}{\frac{1}{x}-\frac{1}{y}}$$

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

$$1-\frac{\frac{x+y}{xy}}{\frac{y}{xy}-\frac{x}{xy}}$$

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

$$1-\frac{\frac{x+y}{xy}}{\frac{y-x}{xy}}$$

Divide \frac{x+y}{xy} by \frac{y-x}{xy} by multiplying \frac{x+y}{xy} by the reciprocal of \frac{y-x}{xy}.

$$1-\frac{\left(x+y\right)xy}{xy\left(y-x\right)}$$

Cancel out xy in both numerator and denominator.

$$1-\frac{x+y}{-x+y}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{-x+y}{-x+y}.

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

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

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

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

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

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

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