Solve -frac{sqrt{10}}{b}+2/3div5/6

$$- \frac { \sqrt { 10 } } { b } + \frac { 2 } { 3 } \div \frac { 5 } { 6 }$$

Evaluate

$$\frac{4}{5}-\frac{\sqrt{10}}{b}$$

Short Solution Steps

Divide \frac{2}{3} by \frac{5}{6} by multiplying \frac{2}{3} by the reciprocal of \frac{5}{6}.

$$-\frac{\sqrt{10}}{b}+\frac{2}{3}\times \frac{6}{5}$$

Multiply \frac{2}{3} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{\sqrt{10}}{b}+\frac{2\times 6}{3\times 5}$$

Do the multiplications in the fraction \frac{2\times 6}{3\times 5}.

$$-\frac{\sqrt{10}}{b}+\frac{12}{15}$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$-\frac{\sqrt{10}}{b}+\frac{4}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and 5 is 5b. Multiply -\frac{\sqrt{10}}{b} times \frac{5}{5}. Multiply \frac{4}{5} times \frac{b}{b}.

$$-\frac{5\sqrt{10}}{5b}+\frac{4b}{5b}$$

Since -\frac{5\sqrt{10}}{5b} and \frac{4b}{5b} have the same denominator, add them by adding their numerators.

$$\frac{-5\sqrt{10}+4b}{5b}$$

Factor

$$\frac{4b-5\sqrt{10}}{5b}$$