Solve a/a-3-9a+8/a^2-3a

$$\frac { a } { a - 3 } - \frac { 9 a + 8 } { a ^ { 2 } - 3 a }$$

Evaluate

$$\frac{a^{2}-9a-8}{a\left(a-3\right)}$$

Short Solution Steps

Factor a^{2}-3a.

$$\frac{a}{a-3}-\frac{9a+8}{a\left(a-3\right)}$$

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

$$\frac{aa}{a\left(a-3\right)}-\frac{9a+8}{a\left(a-3\right)}$$

Since \frac{aa}{a\left(a-3\right)} and \frac{9a+8}{a\left(a-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{aa-\left(9a+8\right)}{a\left(a-3\right)}$$

Do the multiplications in aa-\left(9a+8\right).

$$\frac{a^{2}-9a-8}{a\left(a-3\right)}$$

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

$$\frac{a^{2}-9a-8}{a^{2}-3a}$$

Expand

$$\frac{a^{2}-9a-8}{a\left(a-3\right)}$$

Short Solution Steps

Factor a^{2}-3a.

$$\frac{a}{a-3}-\frac{9a+8}{a\left(a-3\right)}$$

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

$$\frac{aa}{a\left(a-3\right)}-\frac{9a+8}{a\left(a-3\right)}$$

Since \frac{aa}{a\left(a-3\right)} and \frac{9a+8}{a\left(a-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{aa-\left(9a+8\right)}{a\left(a-3\right)}$$

Do the multiplications in aa-\left(9a+8\right).

$$\frac{a^{2}-9a-8}{a\left(a-3\right)}$$

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

$$\frac{a^{2}-9a-8}{a^{2}-3a}$$