Solve 3/w+7/x/frac{7{w}-3/x}

$$\frac { \frac { 3 } { w } + \frac { 7 } { x } } { \frac { 7 } { w } - \frac { 3 } { x } }$$

Evaluate

$$\frac{3x+7w}{7x-3w}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of w and x is wx. Multiply \frac{3}{w} times \frac{x}{x}. Multiply \frac{7}{x} times \frac{w}{w}.

$$\frac{\frac{3x}{wx}+\frac{7w}{wx}}{\frac{7}{w}-\frac{3}{x}}$$

Since \frac{3x}{wx} and \frac{7w}{wx} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3x+7w}{wx}}{\frac{7}{w}-\frac{3}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of w and x is wx. Multiply \frac{7}{w} times \frac{x}{x}. Multiply \frac{3}{x} times \frac{w}{w}.

$$\frac{\frac{3x+7w}{wx}}{\frac{7x}{wx}-\frac{3w}{wx}}$$

Since \frac{7x}{wx} and \frac{3w}{wx} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3x+7w}{wx}}{\frac{7x-3w}{wx}}$$

Divide \frac{3x+7w}{wx} by \frac{7x-3w}{wx} by multiplying \frac{3x+7w}{wx} by the reciprocal of \frac{7x-3w}{wx}.

$$\frac{\left(3x+7w\right)wx}{wx\left(7x-3w\right)}$$

Cancel out wx in both numerator and denominator.

$$\frac{3x+7w}{7x-3w}$$

Expand

$$\frac{3x+7w}{7x-3w}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of w and x is wx. Multiply \frac{3}{w} times \frac{x}{x}. Multiply \frac{7}{x} times \frac{w}{w}.

$$\frac{\frac{3x}{wx}+\frac{7w}{wx}}{\frac{7}{w}-\frac{3}{x}}$$

Since \frac{3x}{wx} and \frac{7w}{wx} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3x+7w}{wx}}{\frac{7}{w}-\frac{3}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of w and x is wx. Multiply \frac{7}{w} times \frac{x}{x}. Multiply \frac{3}{x} times \frac{w}{w}.

$$\frac{\frac{3x+7w}{wx}}{\frac{7x}{wx}-\frac{3w}{wx}}$$

Since \frac{7x}{wx} and \frac{3w}{wx} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3x+7w}{wx}}{\frac{7x-3w}{wx}}$$

Divide \frac{3x+7w}{wx} by \frac{7x-3w}{wx} by multiplying \frac{3x+7w}{wx} by the reciprocal of \frac{7x-3w}{wx}.

$$\frac{\left(3x+7w\right)wx}{wx\left(7x-3w\right)}$$

Cancel out wx in both numerator and denominator.

$$\frac{3x+7w}{7x-3w}$$