Solve 1+2/x/frac{3{y}-4/x}

$$\frac { 1 + \frac { 2 } { x } } { \frac { 3 } { y } - \frac { 4 } { x } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{3}{y} times \frac{x}{x}. Multiply \frac{4}{x} times \frac{y}{y}.

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

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

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{3}{y} times \frac{x}{x}. Multiply \frac{4}{x} times \frac{y}{y}.

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

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

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