Solve n/3n-3n/n*3n/n-3n

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

Evaluate

$$\frac{29}{6}\approx 4.833333333$$

Solution Steps

Cancel out n in both numerator and denominator.

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

Cancel out n in both numerator and denominator.

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

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

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

Cancel out n in both numerator and denominator.

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

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

$$\frac{1}{3}-3\left(-\frac{3}{2}\right)$$

Express 3\left(-\frac{3}{2}\right) as a single fraction.

$$\frac{1}{3}-\frac{3\left(-3\right)}{2}$$

Multiply 3 and -3 to get -9.

$$\frac{1}{3}-\frac{-9}{2}$$

Fraction \frac{-9}{2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$\frac{1}{3}-\left(-\frac{9}{2}\right)$$

The opposite of -\frac{9}{2} is \frac{9}{2}.

$$\frac{1}{3}+\frac{9}{2}$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{9}{2} to fractions with denominator 6.

$$\frac{2}{6}+\frac{27}{6}$$

Since \frac{2}{6} and \frac{27}{6} have the same denominator, add them by adding their numerators.

$$\frac{2+27}{6}$$

Add 2 and 27 to get 29.

$$\frac{29}{6}$$

Factor

$$\frac{29}{2 \cdot 3} = 4\frac{5}{6} = 4.833333333333333$$