Solve (n/3n-3n/n)3n/n-3n

$$( \frac{ n }{ 3n } - \frac{ 3n }{ n } ) \frac{ 3n }{ n-3n }$$

Evaluate

$$4$$

Solution Steps

Cancel out n in both numerator and denominator.

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

Cancel out n in both numerator and denominator.

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

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

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

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

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

Subtract 9 from 1 to get -8.

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

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

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

Cancel out n 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

$$2^{2}$$