Solve 5/y-1/x/frac{1{y^2}-7/x}

$$\frac { \frac { 5 } { y } - \frac { 1 } { x } } { \frac { 1 } { y ^ { 2 } } - \frac { 7 } { x } }$$

Evaluate

$$\frac{y\left(5x-y\right)}{x-7y^{2}}$$

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{5}{y} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{y}{y}.

$$\frac{\frac{5x}{xy}-\frac{y}{xy}}{\frac{1}{y^{2}}-\frac{7}{x}}$$

Since \frac{5x}{xy} and \frac{y}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5x-y}{xy}}{\frac{1}{y^{2}}-\frac{7}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y^{2} and x is xy^{2}. Multiply \frac{1}{y^{2}} times \frac{x}{x}. Multiply \frac{7}{x} times \frac{y^{2}}{y^{2}}.

$$\frac{\frac{5x-y}{xy}}{\frac{x}{xy^{2}}-\frac{7y^{2}}{xy^{2}}}$$

Since \frac{x}{xy^{2}} and \frac{7y^{2}}{xy^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5x-y}{xy}}{\frac{x-7y^{2}}{xy^{2}}}$$

Divide \frac{5x-y}{xy} by \frac{x-7y^{2}}{xy^{2}} by multiplying \frac{5x-y}{xy} by the reciprocal of \frac{x-7y^{2}}{xy^{2}}.

$$\frac{\left(5x-y\right)xy^{2}}{xy\left(x-7y^{2}\right)}$$

Cancel out xy in both numerator and denominator.

$$\frac{y\left(5x-y\right)}{x-7y^{2}}$$

Use the distributive property to multiply y by 5x-y.

$$\frac{5yx-y^{2}}{x-7y^{2}}$$

Expand

$$\frac{5xy-y^{2}}{x-7y^{2}}$$

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{5}{y} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{y}{y}.

$$\frac{\frac{5x}{xy}-\frac{y}{xy}}{\frac{1}{y^{2}}-\frac{7}{x}}$$

Since \frac{5x}{xy} and \frac{y}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5x-y}{xy}}{\frac{1}{y^{2}}-\frac{7}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y^{2} and x is xy^{2}. Multiply \frac{1}{y^{2}} times \frac{x}{x}. Multiply \frac{7}{x} times \frac{y^{2}}{y^{2}}.

$$\frac{\frac{5x-y}{xy}}{\frac{x}{xy^{2}}-\frac{7y^{2}}{xy^{2}}}$$

Since \frac{x}{xy^{2}} and \frac{7y^{2}}{xy^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5x-y}{xy}}{\frac{x-7y^{2}}{xy^{2}}}$$

Divide \frac{5x-y}{xy} by \frac{x-7y^{2}}{xy^{2}} by multiplying \frac{5x-y}{xy} by the reciprocal of \frac{x-7y^{2}}{xy^{2}}.

$$\frac{\left(5x-y\right)xy^{2}}{xy\left(x-7y^{2}\right)}$$

Cancel out xy in both numerator and denominator.

$$\frac{y\left(5x-y\right)}{x-7y^{2}}$$

Use the distributive property to multiply y by 5x-y.

$$\frac{5yx-y^{2}}{x-7y^{2}}$$