Solve 3/4-1/x/frac{1{3x}-1/4}

$$\frac { \frac { 3 } { 4 } - \frac { 1 } { x } } { \frac { 1 } { 3 x } - \frac { 1 } { 4 } }$$

Evaluate

$$-3$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and x is 4x. Multiply \frac{3}{4} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{4}{4}.

$$\frac{\frac{3x}{4x}-\frac{4}{4x}}{\frac{1}{3x}-\frac{1}{4}}$$

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

$$\frac{\frac{3x-4}{4x}}{\frac{1}{3x}-\frac{1}{4}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x and 4 is 12x. Multiply \frac{1}{3x} times \frac{4}{4}. Multiply \frac{1}{4} times \frac{3x}{3x}.

$$\frac{\frac{3x-4}{4x}}{\frac{4}{12x}-\frac{3x}{12x}}$$

Since \frac{4}{12x} and \frac{3x}{12x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3x-4}{4x}}{\frac{4-3x}{12x}}$$

Divide \frac{3x-4}{4x} by \frac{4-3x}{12x} by multiplying \frac{3x-4}{4x} by the reciprocal of \frac{4-3x}{12x}.

$$\frac{\left(3x-4\right)\times 12x}{4x\left(4-3x\right)}$$

Extract the negative sign in 3x-4.

$$\frac{-12x\left(-3x+4\right)}{4x\left(-3x+4\right)}$$

Cancel out 4x\left(-3x+4\right) in both numerator and denominator.

$$-3$$

Factor

$$-3$$