Solve 3/6a-10-15/9a^2-25

$$\frac { 3 } { 6 a - 10 } - \frac { 15 } { 9 a ^ { 2 } - 25 }$$

Evaluate

$$\frac{3}{2\left(3a+5\right)}$$

Short Solution Steps

Factor 6a-10. Factor 9a^{2}-25.

$$\frac{3}{2\left(3a-5\right)}-\frac{15}{\left(3a-5\right)\left(3a+5\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(3a-5\right) and \left(3a-5\right)\left(3a+5\right) is 2\left(3a-5\right)\left(3a+5\right). Multiply \frac{3}{2\left(3a-5\right)} times \frac{3a+5}{3a+5}. Multiply \frac{15}{\left(3a-5\right)\left(3a+5\right)} times \frac{2}{2}.

$$\frac{3\left(3a+5\right)}{2\left(3a-5\right)\left(3a+5\right)}-\frac{15\times 2}{2\left(3a-5\right)\left(3a+5\right)}$$

Since \frac{3\left(3a+5\right)}{2\left(3a-5\right)\left(3a+5\right)} and \frac{15\times 2}{2\left(3a-5\right)\left(3a+5\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(3a+5\right)-15\times 2}{2\left(3a-5\right)\left(3a+5\right)}$$

Do the multiplications in 3\left(3a+5\right)-15\times 2.

$$\frac{9a+15-30}{2\left(3a-5\right)\left(3a+5\right)}$$

Combine like terms in 9a+15-30.

$$\frac{9a-15}{2\left(3a-5\right)\left(3a+5\right)}$$

Factor the expressions that are not already factored in \frac{9a-15}{2\left(3a-5\right)\left(3a+5\right)}.

$$\frac{3\left(3a-5\right)}{2\left(3a-5\right)\left(3a+5\right)}$$

Cancel out 3a-5 in both numerator and denominator.

$$\frac{3}{2\left(3a+5\right)}$$

Expand 2\left(3a+5\right).

$$\frac{3}{6a+10}$$

Factor

$$\frac{3}{2\left(3a+5\right)}$$