Solve 49x^2-y^2/xy/frac{7{y}-1/x}

$$\frac{ \frac{ 49 { x }^{ 2 } - { y }^{ 2 } }{ xy } }{ \frac{ 7 }{ y } - \frac{ 1 }{ x } }$$

Evaluate

$$7x+y$$

Short Solution Steps

Express \frac{\frac{49x^{2}-y^{2}}{xy}}{\frac{7}{y}-\frac{1}{x}} as a single fraction.

$$\frac{49x^{2}-y^{2}}{xy\left(\frac{7}{y}-\frac{1}{x}\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{7}{y} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{y}{y}.

$$\frac{49x^{2}-y^{2}}{xy\left(\frac{7x}{xy}-\frac{y}{xy}\right)}$$

Since \frac{7x}{xy} and \frac{y}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{49x^{2}-y^{2}}{xy\times \frac{7x-y}{xy}}$$

Express x\times \frac{7x-y}{xy} as a single fraction.

$$\frac{49x^{2}-y^{2}}{\frac{x\left(7x-y\right)}{xy}y}$$

Cancel out x in both numerator and denominator.

$$\frac{49x^{2}-y^{2}}{\frac{7x-y}{y}y}$$

Cancel out y and y.

$$\frac{49x^{2}-y^{2}}{7x-y}$$

Factor the expressions that are not already factored.

$$\frac{\left(7x+y\right)\left(7x-y\right)}{7x-y}$$

Cancel out 7x-y in both numerator and denominator.

$$7x+y$$

Expand

$$7x+y$$

Short Solution Steps

Express \frac{\frac{49x^{2}-y^{2}}{xy}}{\frac{7}{y}-\frac{1}{x}} as a single fraction.

$$\frac{49x^{2}-y^{2}}{xy\left(\frac{7}{y}-\frac{1}{x}\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{7}{y} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{y}{y}.

$$\frac{49x^{2}-y^{2}}{xy\left(\frac{7x}{xy}-\frac{y}{xy}\right)}$$

Since \frac{7x}{xy} and \frac{y}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{49x^{2}-y^{2}}{xy\times \frac{7x-y}{xy}}$$

Express x\times \frac{7x-y}{xy} as a single fraction.

$$\frac{49x^{2}-y^{2}}{\frac{x\left(7x-y\right)}{xy}y}$$

Cancel out x in both numerator and denominator.

$$\frac{49x^{2}-y^{2}}{\frac{7x-y}{y}y}$$

Cancel out y and y.

$$\frac{49x^{2}-y^{2}}{7x-y}$$

Factor the expressions that are not already factored.

$$\frac{\left(7x+y\right)\left(7x-y\right)}{7x-y}$$

Cancel out 7x-y in both numerator and denominator.

$$7x+y$$