Solve b-3/ab+b-3/ab+a+bb/3a+9+5b/2a

$$\frac { b - 3 } { a b } + \frac { b - 3 } { a b } + \frac { a + b b } { 3 a } + \frac { 9 + 5 b } { 2 a }$$

Evaluate

$$\frac{2ab+2b^{3}+15b^{2}+39b-36}{6ab}$$

Short Solution Steps

Multiply b and b to get b^{2}.

$$\frac{b-3}{ab}+\frac{b-3}{ab}+\frac{a+b^{2}}{3a}+\frac{9+5b}{2a}$$

Combine \frac{b-3}{ab} and \frac{b-3}{ab} to get 2\times \frac{b-3}{ab}.

$$2\times \frac{b-3}{ab}+\frac{a+b^{2}}{3a}+\frac{9+5b}{2a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a and 2a is 6a. Multiply \frac{a+b^{2}}{3a} times \frac{2}{2}. Multiply \frac{9+5b}{2a} times \frac{3}{3}.

$$2\times \frac{b-3}{ab}+\frac{2\left(a+b^{2}\right)}{6a}+\frac{3\left(9+5b\right)}{6a}$$

Since \frac{2\left(a+b^{2}\right)}{6a} and \frac{3\left(9+5b\right)}{6a} have the same denominator, add them by adding their numerators.

$$2\times \frac{b-3}{ab}+\frac{2\left(a+b^{2}\right)+3\left(9+5b\right)}{6a}$$

Do the multiplications in 2\left(a+b^{2}\right)+3\left(9+5b\right).

$$2\times \frac{b-3}{ab}+\frac{2a+2b^{2}+27+15b}{6a}$$

Express 2\times \frac{b-3}{ab} as a single fraction.

$$\frac{2\left(b-3\right)}{ab}+\frac{2a+2b^{2}+27+15b}{6a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of ab and 6a is 6ab. Multiply \frac{2\left(b-3\right)}{ab} times \frac{6}{6}. Multiply \frac{2a+2b^{2}+27+15b}{6a} times \frac{b}{b}.

$$\frac{6\times 2\left(b-3\right)}{6ab}+\frac{\left(2a+2b^{2}+27+15b\right)b}{6ab}$$

Since \frac{6\times 2\left(b-3\right)}{6ab} and \frac{\left(2a+2b^{2}+27+15b\right)b}{6ab} have the same denominator, add them by adding their numerators.

$$\frac{6\times 2\left(b-3\right)+\left(2a+2b^{2}+27+15b\right)b}{6ab}$$

Do the multiplications in 6\times 2\left(b-3\right)+\left(2a+2b^{2}+27+15b\right)b.

$$\frac{12b-36+2ab+2b^{3}+27b+15b^{2}}{6ab}$$

Combine like terms in 12b-36+2ab+2b^{3}+27b+15b^{2}.

$$\frac{39b-36+2ab+2b^{3}+15b^{2}}{6ab}$$

Expand

$$\frac{2ab+2b^{3}+15b^{2}+39b-36}{6ab}$$

Short Solution Steps

Multiply b and b to get b^{2}.

$$\frac{b-3}{ab}+\frac{b-3}{ab}+\frac{a+b^{2}}{3a}+\frac{9+5b}{2a}$$

Combine \frac{b-3}{ab} and \frac{b-3}{ab} to get 2\times \frac{b-3}{ab}.

$$2\times \frac{b-3}{ab}+\frac{a+b^{2}}{3a}+\frac{9+5b}{2a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a and 2a is 6a. Multiply \frac{a+b^{2}}{3a} times \frac{2}{2}. Multiply \frac{9+5b}{2a} times \frac{3}{3}.

$$2\times \frac{b-3}{ab}+\frac{2\left(a+b^{2}\right)}{6a}+\frac{3\left(9+5b\right)}{6a}$$

Since \frac{2\left(a+b^{2}\right)}{6a} and \frac{3\left(9+5b\right)}{6a} have the same denominator, add them by adding their numerators.

$$2\times \frac{b-3}{ab}+\frac{2\left(a+b^{2}\right)+3\left(9+5b\right)}{6a}$$

Do the multiplications in 2\left(a+b^{2}\right)+3\left(9+5b\right).

$$2\times \frac{b-3}{ab}+\frac{2a+2b^{2}+27+15b}{6a}$$

Express 2\times \frac{b-3}{ab} as a single fraction.

$$\frac{2\left(b-3\right)}{ab}+\frac{2a+2b^{2}+27+15b}{6a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of ab and 6a is 6ab. Multiply \frac{2\left(b-3\right)}{ab} times \frac{6}{6}. Multiply \frac{2a+2b^{2}+27+15b}{6a} times \frac{b}{b}.

$$\frac{6\times 2\left(b-3\right)}{6ab}+\frac{\left(2a+2b^{2}+27+15b\right)b}{6ab}$$

Since \frac{6\times 2\left(b-3\right)}{6ab} and \frac{\left(2a+2b^{2}+27+15b\right)b}{6ab} have the same denominator, add them by adding their numerators.

$$\frac{6\times 2\left(b-3\right)+\left(2a+2b^{2}+27+15b\right)b}{6ab}$$

Do the multiplications in 6\times 2\left(b-3\right)+\left(2a+2b^{2}+27+15b\right)b.

$$\frac{12b-36+2ab+2b^{3}+27b+15b^{2}}{6ab}$$

Combine like terms in 12b-36+2ab+2b^{3}+27b+15b^{2}.

$$\frac{39b-36+2ab+2b^{3}+15b^{2}}{6ab}$$