Solve 69/a^2-b^2-6/a+b

$$\frac { 69 } { a ^ { 2 } - b ^ { 2 } } - \frac { 6 } { a + b }$$

Evaluate

$$\frac{3\left(23+2b-2a\right)}{a^{2}-b^{2}}$$

Short Solution Steps

Factor a^{2}-b^{2}.

$$\frac{69}{\left(a+b\right)\left(a-b\right)}-\frac{6}{a+b}$$

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

$$\frac{69}{\left(a+b\right)\left(a-b\right)}-\frac{6\left(a-b\right)}{\left(a+b\right)\left(a-b\right)}$$

Since \frac{69}{\left(a+b\right)\left(a-b\right)} and \frac{6\left(a-b\right)}{\left(a+b\right)\left(a-b\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{69-6\left(a-b\right)}{\left(a+b\right)\left(a-b\right)}$$

Do the multiplications in 69-6\left(a-b\right).

$$\frac{69-6a+6b}{\left(a+b\right)\left(a-b\right)}$$

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

$$\frac{69-6a+6b}{a^{2}-b^{2}}$$

Factor

$$\frac{3\left(23+2b-2a\right)}{\left(a-b\right)\left(a+b\right)}$$