Solve (a+3b/a^2-3ab-1/a)

$$( \frac { a + 3 b } { a ^ { 2 } - 3 a b } - \frac { 1 } { a } )$$

Evaluate

$$\frac{6b}{a\left(a-3b\right)}$$

Short Solution Steps

Factor a^{2}-3ab.

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

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

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

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

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

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

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

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

$$\frac{6b}{a\left(a-3b\right)}$$

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

$$\frac{6b}{a^{2}-3ab}$$

Expand

$$\frac{6b}{a^{2}-3ab}$$

Short Solution Steps

Factor a^{2}-3ab.

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

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

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

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

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

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

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

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

$$\frac{6b}{a\left(a-3b\right)}$$

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

$$\frac{6b}{a^{2}-3ab}$$