Solve 3a/a^2-9-2b/ab+3b-b/ab-3b=

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

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{2b}{ab+3b}.

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

Cancel out b in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{b}{ab-3b}.

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

Cancel out b in both numerator and denominator.

$$\frac{3a}{a^{2}-9}-\frac{2}{a+3}-\frac{1}{a-3}$$

Factor a^{2}-9.

$$\frac{3a}{\left(a-3\right)\left(a+3\right)}-\frac{2}{a+3}-\frac{1}{a-3}$$

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

$$\frac{3a}{\left(a-3\right)\left(a+3\right)}-\frac{2\left(a-3\right)}{\left(a-3\right)\left(a+3\right)}-\frac{1}{a-3}$$

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

$$\frac{3a-2\left(a-3\right)}{\left(a-3\right)\left(a+3\right)}-\frac{1}{a-3}$$

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

$$\frac{3a-2a+6}{\left(a-3\right)\left(a+3\right)}-\frac{1}{a-3}$$

Combine like terms in 3a-2a+6.

$$\frac{a+6}{\left(a-3\right)\left(a+3\right)}-\frac{1}{a-3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(a-3\right)\left(a+3\right) and a-3 is \left(a-3\right)\left(a+3\right). Multiply \frac{1}{a-3} times \frac{a+3}{a+3}.

$$\frac{a+6}{\left(a-3\right)\left(a+3\right)}-\frac{a+3}{\left(a-3\right)\left(a+3\right)}$$

Since \frac{a+6}{\left(a-3\right)\left(a+3\right)} and \frac{a+3}{\left(a-3\right)\left(a+3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a+6-\left(a+3\right)}{\left(a-3\right)\left(a+3\right)}$$

Do the multiplications in a+6-\left(a+3\right).

$$\frac{a+6-a-3}{\left(a-3\right)\left(a+3\right)}$$

Combine like terms in a+6-a-3.

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

Expand \left(a-3\right)\left(a+3\right).

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

Differentiate w.r.t. a

$$-\frac{6a}{\left(a^{2}-9\right)^{2}}$$