Solve (x/3x-3x/x)*3x/x-3x

$$( \frac{ x }{ 3x } - \frac{ 3x }{ x } ) \times \frac{ 3x }{ x-3x }$$

Evaluate

$$4$$

Solution Steps

Cancel out x in both numerator and denominator.

$$\left(\frac{1}{3}-\frac{3x}{x}\right)\times \frac{3x}{x-3x}$$

Cancel out x in both numerator and denominator.

$$\left(\frac{1}{3}-3\right)\times \frac{3x}{x-3x}$$

Convert 3 to fraction \frac{9}{3}.

$$\left(\frac{1}{3}-\frac{9}{3}\right)\times \frac{3x}{x-3x}$$

Since \frac{1}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-9}{3}\times \frac{3x}{x-3x}$$

Subtract 9 from 1 to get -8.

$$-\frac{8}{3}\times \frac{3x}{x-3x}$$

Combine x and -3x to get -2x.

$$-\frac{8}{3}\times \frac{3x}{-2x}$$

Cancel out x in both numerator and denominator.

$$-\frac{8}{3}\times \frac{3}{-2}$$

Fraction \frac{3}{-2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$-\frac{8}{3}\left(-\frac{3}{2}\right)$$

Multiply -\frac{8}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-8\left(-3\right)}{3\times 2}$$

Do the multiplications in the fraction \frac{-8\left(-3\right)}{3\times 2}.

$$\frac{24}{6}$$

Divide 24 by 6 to get 4.

$$4$$

Factor

$$2^{2}$$