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

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{\left(a-2\right)b}{b\left(a+2\right)} and \frac{a^{2}\left(a+2\right)}{b\left(a+2\right)} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Expand b\left(a+2\right).

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

Expand

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

Short Solution Steps

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

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

Since \frac{\left(a-2\right)b}{b\left(a+2\right)} and \frac{a^{2}\left(a+2\right)}{b\left(a+2\right)} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Expand b\left(a+2\right).

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