Solve 6/y+6/x/frac{6{y}-6/x}

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

Evaluate

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

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{6}{y} times \frac{x}{x}. Multiply \frac{6}{x} times \frac{y}{y}.

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

Since \frac{6x}{xy} and \frac{6y}{xy} have the same denominator, add them by adding their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{6}{y} times \frac{x}{x}. Multiply \frac{6}{x} times \frac{y}{y}.

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

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

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

Divide \frac{6x+6y}{xy} by \frac{6x-6y}{xy} by multiplying \frac{6x+6y}{xy} by the reciprocal of \frac{6x-6y}{xy}.

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

Cancel out xy in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out 6 in both numerator and denominator.

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

Expand

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

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{6}{y} times \frac{x}{x}. Multiply \frac{6}{x} times \frac{y}{y}.

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

Since \frac{6x}{xy} and \frac{6y}{xy} have the same denominator, add them by adding their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{6}{y} times \frac{x}{x}. Multiply \frac{6}{x} times \frac{y}{y}.

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

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

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

Divide \frac{6x+6y}{xy} by \frac{6x-6y}{xy} by multiplying \frac{6x+6y}{xy} by the reciprocal of \frac{6x-6y}{xy}.

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

Cancel out xy in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out 6 in both numerator and denominator.

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