Solve 5a/a+b-6/a

$$\frac { 5 a } { a + b } - \frac { 6 } { a }$$

Evaluate

$$\frac{5a^{2}-6a-6b}{a\left(a+b\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a+b and a is a\left(a+b\right). Multiply \frac{5a}{a+b} times \frac{a}{a}. Multiply \frac{6}{a} times \frac{a+b}{a+b}.

$$\frac{5aa}{a\left(a+b\right)}-\frac{6\left(a+b\right)}{a\left(a+b\right)}$$

Since \frac{5aa}{a\left(a+b\right)} and \frac{6\left(a+b\right)}{a\left(a+b\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5aa-6\left(a+b\right)}{a\left(a+b\right)}$$

Do the multiplications in 5aa-6\left(a+b\right).

$$\frac{5a^{2}-6a-6b}{a\left(a+b\right)}$$

Expand a\left(a+b\right).

$$\frac{5a^{2}-6a-6b}{a^{2}+ab}$$

Factor

$$\frac{5a^{2}-6a-6b}{a\left(a+b\right)}$$