Solve 3a+2b/a^2-b^2-a/a^2-b^2

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

Evaluate

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

Short Solution Steps

Since \frac{3a+2b}{a^{2}-b^{2}} and \frac{a}{a^{2}-b^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Factor the expressions that are not already factored in \frac{2a+2b}{a^{2}-b^{2}}.

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

Cancel out a+b in both numerator and denominator.

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

Expand

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

Short Solution Steps

Since \frac{3a+2b}{a^{2}-b^{2}} and \frac{a}{a^{2}-b^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Factor the expressions that are not already factored in \frac{2a+2b}{a^{2}-b^{2}}.

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

Cancel out a+b in both numerator and denominator.

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