Solve 1/x+1/y/1-frac{9{xy}}

$$\frac { \frac { 1 } { x } + \frac { 1 } { y } } { 1 - \frac { 9 } { x y } }$$

Evaluate

$$\frac{x+y}{xy-9}$$

Solution Steps

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}.

$$\frac{\frac{y}{xy}+\frac{x}{xy}}{1-\frac{9}{xy}}$$

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

$$\frac{\frac{y+x}{xy}}{1-\frac{9}{xy}}$$

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

$$\frac{\frac{y+x}{xy}}{\frac{xy}{xy}-\frac{9}{xy}}$$

Since \frac{xy}{xy} and \frac{9}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{y+x}{xy}}{\frac{xy-9}{xy}}$$

Divide \frac{y+x}{xy} by \frac{xy-9}{xy} by multiplying \frac{y+x}{xy} by the reciprocal of \frac{xy-9}{xy}.

$$\frac{\left(y+x\right)xy}{xy\left(xy-9\right)}$$

Cancel out xy in both numerator and denominator.

$$\frac{x+y}{xy-9}$$

Expand

$$\frac{x+y}{xy-9}$$

Solution Steps

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}.

$$\frac{\frac{y}{xy}+\frac{x}{xy}}{1-\frac{9}{xy}}$$

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

$$\frac{\frac{y+x}{xy}}{1-\frac{9}{xy}}$$

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

$$\frac{\frac{y+x}{xy}}{\frac{xy}{xy}-\frac{9}{xy}}$$

Since \frac{xy}{xy} and \frac{9}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{y+x}{xy}}{\frac{xy-9}{xy}}$$

Divide \frac{y+x}{xy} by \frac{xy-9}{xy} by multiplying \frac{y+x}{xy} by the reciprocal of \frac{xy-9}{xy}.

$$\frac{\left(y+x\right)xy}{xy\left(xy-9\right)}$$

Cancel out xy in both numerator and denominator.

$$\frac{x+y}{xy-9}$$