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

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

Evaluate

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

Short 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{2}{y} times \frac{x}{x}.

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

Since \frac{y}{xy} and \frac{2x}{xy} have the same denominator, add them by adding their numerators.

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

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

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

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

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

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

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

Cancel out xy in both numerator and denominator.

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

Use the distributive property to multiply y by 2x+y.

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

Expand

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

Short 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{2}{y} times \frac{x}{x}.

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

Since \frac{y}{xy} and \frac{2x}{xy} have the same denominator, add them by adding their numerators.

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

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

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

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

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

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

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

Cancel out xy in both numerator and denominator.

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

Use the distributive property to multiply y by 2x+y.

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