Solve (3(2/x))/((frac{2{x})-1)}

$$\frac{ (3( \frac{ 2 }{ x } )) }{ (( \frac{ 2 }{ x } )-1) }$$

Evaluate

$$-\frac{6}{x-2}$$

Solution Steps

Express 3\times \frac{2}{x} as a single fraction.

$$\frac{\frac{3\times 2}{x}}{\frac{2}{x}-1}$$

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

$$\frac{\frac{3\times 2}{x}}{\frac{2}{x}-\frac{x}{x}}$$

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

$$\frac{\frac{3\times 2}{x}}{\frac{2-x}{x}}$$

Divide \frac{3\times 2}{x} by \frac{2-x}{x} by multiplying \frac{3\times 2}{x} by the reciprocal of \frac{2-x}{x}.

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

Cancel out x in both numerator and denominator.

$$\frac{2\times 3}{-x+2}$$

Multiply 2 and 3 to get 6.

$$\frac{6}{-x+2}$$

Differentiate w.r.t. x

$$\frac{6}{\left(x-2\right)^{2}}$$