Solve frac{6a^{5}}{5b^{3}}*b^2/4a^4+a^2/b^2*b/2a

$$\frac { 6 a ^ { 5 } } { 5 b ^ { 3 } } \times \frac { b ^ { 2 } } { 4 a ^ { 4 } } + \frac { a ^ { 2 } } { b ^ { 2 } } \times \frac { b } { 2 a }$$

Evaluate

$$\frac{4a}{5b}$$

Short Solution Steps

Multiply \frac{6a^{5}}{5b^{3}} times \frac{b^{2}}{4a^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6a^{5}b^{2}}{5b^{3}\times 4a^{4}}+\frac{a^{2}}{b^{2}}\times \frac{b}{2a}$$

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

$$\frac{3a}{2\times 5b}+\frac{a^{2}}{b^{2}}\times \frac{b}{2a}$$

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

$$\frac{3a}{2\times 5b}+\frac{a^{2}b}{b^{2}\times 2a}$$

Cancel out ab in both numerator and denominator.

$$\frac{3a}{2\times 5b}+\frac{a}{2b}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\times 5b and 2b is 2\times 5b. Multiply \frac{a}{2b} times \frac{5}{5}.

$$\frac{3a}{2\times 5b}+\frac{5a}{2\times 5b}$$

Since \frac{3a}{2\times 5b} and \frac{5a}{2\times 5b} have the same denominator, add them by adding their numerators.

$$\frac{3a+5a}{2\times 5b}$$

Combine like terms in 3a+5a.

$$\frac{8a}{2\times 5b}$$

Cancel out 2 in both numerator and denominator.

$$\frac{4a}{5b}$$

Differentiate w.r.t. a

$$\frac{4}{5b}$$