Solve 2a+3b/b+b/2a-3b=

$$\frac { 2 a + 3 b } { b } + \frac { b } { 2 a - 3 b } =$$

Evaluate

$$\frac{4\left(a^{2}-2b^{2}\right)}{b\left(2a-3b\right)}$$

Short Solution Steps

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

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

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

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

Do the multiplications in \left(2a+3b\right)\left(2a-3b\right)+bb.

$$\frac{4a^{2}-6ab+6ba-9b^{2}+b^{2}}{b\left(2a-3b\right)}$$

Combine like terms in 4a^{2}-6ab+6ba-9b^{2}+b^{2}.

$$\frac{4a^{2}-8b^{2}}{b\left(2a-3b\right)}$$

Expand b\left(2a-3b\right).

$$\frac{4a^{2}-8b^{2}}{2ab-3b^{2}}$$

Expand

$$-\frac{4\left(2b^{2}-a^{2}\right)}{b\left(2a-3b\right)}$$

Short Solution Steps

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

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

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

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

Do the multiplications in \left(2a+3b\right)\left(2a-3b\right)+bb.

$$\frac{4a^{2}-6ab+6ba-9b^{2}+b^{2}}{b\left(2a-3b\right)}$$

Combine like terms in 4a^{2}-6ab+6ba-9b^{2}+b^{2}.

$$\frac{4a^{2}-8b^{2}}{b\left(2a-3b\right)}$$

Expand b\left(2a-3b\right).

$$\frac{4a^{2}-8b^{2}}{2ab-3b^{2}}$$