Solve c/a+b+c/a-b

$$\frac { c } { a + b } + \frac { c } { a - b }$$

Evaluate

$$\frac{2ac}{a^{2}-b^{2}}$$

$$|a|\neq |b|$$

Short Solution Steps

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

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

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

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

Do the multiplications in c\left(a-b\right)+c\left(a+b\right).

$$\frac{ca-cb+ca+cb}{\left(a+b\right)\left(a-b\right)}$$

Combine like terms in ca-cb+ca+cb.

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

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

$$\frac{2ca}{a^{2}-b^{2}}$$

Factor

$$\frac{2ac}{a^{2}-b^{2}}$$