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

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

Evaluate

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

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{-5}{y} times \frac{x}{x}. Multiply \frac{3}{x} times \frac{y}{y}.

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

Since \frac{-5x}{xy} and \frac{3y}{xy} have the same denominator, add them by adding their numerators.

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

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

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

Cancel out xy in both numerator and denominator.

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

Expand

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

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{-5}{y} times \frac{x}{x}. Multiply \frac{3}{x} times \frac{y}{y}.

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

Since \frac{-5x}{xy} and \frac{3y}{xy} have the same denominator, add them by adding their numerators.

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

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

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

Cancel out xy in both numerator and denominator.

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