Solve 5(1^3/3-1)/frac{1{3}-1}

$$\frac { 5 ( \frac { 1 ^ { 3 } } { 3 } - 1 ) } { \frac { 1 } { 3 } - 1 }$$

Evaluate

$$5$$

Solution Steps

Calculate 1 to the power of 3 and get 1.

$$\frac{5\left(\frac{1}{3}-1\right)}{\frac{1}{3}-1}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{5\left(\frac{1}{3}-\frac{3}{3}\right)}{\frac{1}{3}-1}$$

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

$$\frac{5\times \frac{1-3}{3}}{\frac{1}{3}-1}$$

Subtract 3 from 1 to get -2.

$$\frac{5\left(-\frac{2}{3}\right)}{\frac{1}{3}-1}$$

Express 5\left(-\frac{2}{3}\right) as a single fraction.

$$\frac{\frac{5\left(-2\right)}{3}}{\frac{1}{3}-1}$$

Multiply 5 and -2 to get -10.

$$\frac{\frac{-10}{3}}{\frac{1}{3}-1}$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$\frac{-\frac{10}{3}}{\frac{1}{3}-1}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{-\frac{10}{3}}{\frac{1}{3}-\frac{3}{3}}$$

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

$$\frac{-\frac{10}{3}}{\frac{1-3}{3}}$$

Subtract 3 from 1 to get -2.

$$\frac{-\frac{10}{3}}{-\frac{2}{3}}$$

Divide -\frac{10}{3} by -\frac{2}{3} by multiplying -\frac{10}{3} by the reciprocal of -\frac{2}{3}.

$$-\frac{10}{3}\left(-\frac{3}{2}\right)$$

Multiply -\frac{10}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-10\left(-3\right)}{3\times 2}$$

Do the multiplications in the fraction \frac{-10\left(-3\right)}{3\times 2}.

$$\frac{30}{6}$$

Divide 30 by 6 to get 5.

$$5$$

Factor

$$5$$