Solve 3/x-4/y^2/frac{4{y}+5/x}

$$\frac { \frac { 3 } { x } - \frac { 4 } { y ^ { 2 } } } { \frac { 4 } { y } + \frac { 5 } { x } }$$

Evaluate

$$\frac{3y^{2}-4x}{y\left(4x+5y\right)}$$

Short Solution Steps

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{3}{x} times \frac{y^{2}}{y^{2}}. Multiply \frac{4}{y^{2}} times \frac{x}{x}.

$$\frac{\frac{3y^{2}}{xy^{2}}-\frac{4x}{xy^{2}}}{\frac{4}{y}+\frac{5}{x}}$$

Since \frac{3y^{2}}{xy^{2}} and \frac{4x}{xy^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3y^{2}-4x}{xy^{2}}}{\frac{4}{y}+\frac{5}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{4}{y} times \frac{x}{x}. Multiply \frac{5}{x} times \frac{y}{y}.

$$\frac{\frac{3y^{2}-4x}{xy^{2}}}{\frac{4x}{xy}+\frac{5y}{xy}}$$

Since \frac{4x}{xy} and \frac{5y}{xy} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3y^{2}-4x}{xy^{2}}}{\frac{4x+5y}{xy}}$$

Divide \frac{3y^{2}-4x}{xy^{2}} by \frac{4x+5y}{xy} by multiplying \frac{3y^{2}-4x}{xy^{2}} by the reciprocal of \frac{4x+5y}{xy}.

$$\frac{\left(3y^{2}-4x\right)xy}{xy^{2}\left(4x+5y\right)}$$

Cancel out xy in both numerator and denominator.

$$\frac{-4x+3y^{2}}{y\left(4x+5y\right)}$$

Use the distributive property to multiply y by 4x+5y.

$$\frac{-4x+3y^{2}}{4yx+5y^{2}}$$

Expand

$$\frac{3y^{2}-4x}{y\left(4x+5y\right)}$$

Short Solution Steps

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{3}{x} times \frac{y^{2}}{y^{2}}. Multiply \frac{4}{y^{2}} times \frac{x}{x}.

$$\frac{\frac{3y^{2}}{xy^{2}}-\frac{4x}{xy^{2}}}{\frac{4}{y}+\frac{5}{x}}$$

Since \frac{3y^{2}}{xy^{2}} and \frac{4x}{xy^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3y^{2}-4x}{xy^{2}}}{\frac{4}{y}+\frac{5}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{4}{y} times \frac{x}{x}. Multiply \frac{5}{x} times \frac{y}{y}.

$$\frac{\frac{3y^{2}-4x}{xy^{2}}}{\frac{4x}{xy}+\frac{5y}{xy}}$$

Since \frac{4x}{xy} and \frac{5y}{xy} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3y^{2}-4x}{xy^{2}}}{\frac{4x+5y}{xy}}$$

Divide \frac{3y^{2}-4x}{xy^{2}} by \frac{4x+5y}{xy} by multiplying \frac{3y^{2}-4x}{xy^{2}} by the reciprocal of \frac{4x+5y}{xy}.

$$\frac{\left(3y^{2}-4x\right)xy}{xy^{2}\left(4x+5y\right)}$$

Cancel out xy in both numerator and denominator.

$$\frac{-4x+3y^{2}}{y\left(4x+5y\right)}$$

Use the distributive property to multiply y by 4x+5y.

$$\frac{-4x+3y^{2}}{4yx+5y^{2}}$$