Solve 9/2b-3/a^2+b/2a^3)*4a^2b^2=

$$\frac { 9 } { 2 b } - \frac { 3 } { a ^ { 2 } } + \frac { b } { 2 a ^ { 3 } } ) \cdot 4 a ^ { 2 } b ^ { 2 } =$$

Evaluate

$$\frac{9}{2b}+\frac{b}{2a^{3}}-\frac{3}{a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2b and a^{2} is 2ba^{2}. Multiply \frac{9}{2b} times \frac{a^{2}}{a^{2}}. Multiply \frac{3}{a^{2}} times \frac{2b}{2b}.

$$\frac{9a^{2}}{2ba^{2}}-\frac{3\times 2b}{2ba^{2}}+\frac{b}{2a^{3}}$$

Since \frac{9a^{2}}{2ba^{2}} and \frac{3\times 2b}{2ba^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9a^{2}-3\times 2b}{2ba^{2}}+\frac{b}{2a^{3}}$$

Do the multiplications in 9a^{2}-3\times 2b.

$$\frac{9a^{2}-6b}{2ba^{2}}+\frac{b}{2a^{3}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2ba^{2} and 2a^{3} is 2ba^{3}. Multiply \frac{9a^{2}-6b}{2ba^{2}} times \frac{a}{a}. Multiply \frac{b}{2a^{3}} times \frac{b}{b}.

$$\frac{\left(9a^{2}-6b\right)a}{2ba^{3}}+\frac{bb}{2ba^{3}}$$

Since \frac{\left(9a^{2}-6b\right)a}{2ba^{3}} and \frac{bb}{2ba^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\left(9a^{2}-6b\right)a+bb}{2ba^{3}}$$

Do the multiplications in \left(9a^{2}-6b\right)a+bb.

$$\frac{9a^{3}-6ba+b^{2}}{2ba^{3}}$$

Factor

$$\frac{\frac{9a^{3}}{b}+b-6a}{2a^{3}}$$