Solve b^2/4:b^3/12+b/10*b^2/3

$$\frac { b ^ { 2 } } { 4 } : \frac { b ^ { 3 } } { 12 } + \frac { b } { 10 } \cdot \frac { b ^ { 2 } } { 3 }$$

Evaluate

$$\frac{b^{3}}{30}+\frac{3}{b}$$

Short Solution Steps

Divide \frac{b^{2}}{4} by \frac{b^{3}}{12} by multiplying \frac{b^{2}}{4} by the reciprocal of \frac{b^{3}}{12}.

$$\frac{b^{2}\times 12}{4b^{3}}+\frac{b}{10}\times \frac{b^{2}}{3}$$

Cancel out 4b^{2} in both numerator and denominator.

$$\frac{3}{b}+\frac{b}{10}\times \frac{b^{2}}{3}$$

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

$$\frac{3}{b}+\frac{bb^{2}}{10\times 3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and 10\times 3 is 30b. Multiply \frac{3}{b} times \frac{30}{30}. Multiply \frac{bb^{2}}{10\times 3} times \frac{b}{b}.

$$\frac{3\times 30}{30b}+\frac{bb^{2}b}{30b}$$

Since \frac{3\times 30}{30b} and \frac{bb^{2}b}{30b} have the same denominator, add them by adding their numerators.

$$\frac{3\times 30+bb^{2}b}{30b}$$

Do the multiplications in 3\times 30+bb^{2}b.

$$\frac{90+b^{4}}{30b}$$

Factor

$$\frac{b^{4}+90}{30b}$$