Solve 2/a+b+2/a-b-4a/a^2-b^2

$$\frac { 2 } { a + b } + \frac { 2 } { a - b } - \frac { 4 a } { a ^ { 2 } - b ^ { 2 } }$$

Evaluate

$$0$$

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{2}{a+b} times \frac{a-b}{a-b}. Multiply \frac{2}{a-b} times \frac{a+b}{a+b}.

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

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

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

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

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

Combine like terms in 2a-2b+2a+2b.

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

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

$$\frac{4a}{\left(a+b\right)\left(a-b\right)}-\frac{4a}{\left(a+b\right)\left(a-b\right)}$$

Since \frac{4a}{\left(a+b\right)\left(a-b\right)} and \frac{4a}{\left(a+b\right)\left(a-b\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4a-4a}{\left(a+b\right)\left(a-b\right)}$$

Combine like terms in 4a-4a.

$$\frac{0}{\left(a+b\right)\left(a-b\right)}$$

Zero divided by any non-zero term gives zero.

$$0$$

Factor

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