Solve 1/a^2+5a-2/a^2-25-1/15-3a

$$\frac { 1 } { a ^ { 2 } + 5 a } - \frac { 2 } { a ^ { 2 } - 25 } - \frac { 1 } { 15 - 3 a }$$

Evaluate

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

Short Solution Steps

Factor a^{2}+5a. Factor a^{2}-25.

$$\frac{1}{a\left(a+5\right)}-\frac{2}{\left(a-5\right)\left(a+5\right)}-\frac{1}{15-3a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a\left(a+5\right) and \left(a-5\right)\left(a+5\right) is a\left(a-5\right)\left(a+5\right). Multiply \frac{1}{a\left(a+5\right)} times \frac{a-5}{a-5}. Multiply \frac{2}{\left(a-5\right)\left(a+5\right)} times \frac{a}{a}.

$$\frac{a-5}{a\left(a-5\right)\left(a+5\right)}-\frac{2a}{a\left(a-5\right)\left(a+5\right)}-\frac{1}{15-3a}$$

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

$$\frac{a-5-2a}{a\left(a-5\right)\left(a+5\right)}-\frac{1}{15-3a}$$

Combine like terms in a-5-2a.

$$\frac{-a-5}{a\left(a-5\right)\left(a+5\right)}-\frac{1}{15-3a}$$

Extract the negative sign in -a-5.

$$\frac{-\left(a+5\right)}{a\left(a-5\right)\left(a+5\right)}-\frac{1}{15-3a}$$

Cancel out a+5 in both numerator and denominator.

$$\frac{-1}{a\left(a-5\right)}-\frac{1}{15-3a}$$

Factor 15-3a.

$$\frac{-1}{a\left(a-5\right)}-\frac{1}{3\left(-a+5\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a\left(a-5\right) and 3\left(-a+5\right) is 3a\left(a-5\right). Multiply \frac{-1}{a\left(a-5\right)} times \frac{3}{3}. Multiply \frac{1}{3\left(-a+5\right)} times \frac{-a}{-a}.

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

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

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

Do the multiplications in -3-\left(-a\right).

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

Expand 3a\left(a-5\right).

$$\frac{-3+a}{3a^{2}-15a}$$

Factor

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