Solve 10a-8/a^2-a*6+1/a-3=

$$10 \frac { a - 8 } { a ^ { 2 } - a \cdot 6 } + \frac { 1 } { a - 3 } =$$

Evaluate

$$\frac{11a^{2}-116a+240}{a\left(a-6\right)\left(a-3\right)}$$

Short Solution Steps

Express 10\times \frac{a-8}{a^{2}-a\times 6} as a single fraction.

$$\frac{10\left(a-8\right)}{a^{2}-a\times 6}+\frac{1}{a-3}$$

Factor a^{2}-a\times 6.

$$\frac{10\left(a-8\right)}{a\left(a-6\right)}+\frac{1}{a-3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a\left(a-6\right) and a-3 is a\left(a-6\right)\left(a-3\right). Multiply \frac{10\left(a-8\right)}{a\left(a-6\right)} times \frac{a-3}{a-3}. Multiply \frac{1}{a-3} times \frac{a\left(a-6\right)}{a\left(a-6\right)}.

$$\frac{10\left(a-8\right)\left(a-3\right)}{a\left(a-6\right)\left(a-3\right)}+\frac{a\left(a-6\right)}{a\left(a-6\right)\left(a-3\right)}$$

Since \frac{10\left(a-8\right)\left(a-3\right)}{a\left(a-6\right)\left(a-3\right)} and \frac{a\left(a-6\right)}{a\left(a-6\right)\left(a-3\right)} have the same denominator, add them by adding their numerators.

$$\frac{10\left(a-8\right)\left(a-3\right)+a\left(a-6\right)}{a\left(a-6\right)\left(a-3\right)}$$

Do the multiplications in 10\left(a-8\right)\left(a-3\right)+a\left(a-6\right).

$$\frac{10a^{2}-30a-80a+240+a^{2}-6a}{a\left(a-6\right)\left(a-3\right)}$$

Combine like terms in 10a^{2}-30a-80a+240+a^{2}-6a.

$$\frac{11a^{2}-116a+240}{a\left(a-6\right)\left(a-3\right)}$$

Expand a\left(a-6\right)\left(a-3\right).

$$\frac{11a^{2}-116a+240}{a^{3}-9a^{2}+18a}$$

Expand

$$\frac{11a^{2}-116a+240}{\left(a-3\right)\left(a^{2}-6a\right)}$$

Short Solution Steps

Express 10\times \frac{a-8}{a^{2}-a\times 6} as a single fraction.

$$\frac{10\left(a-8\right)}{a^{2}-a\times 6}+\frac{1}{a-3}$$

Factor a^{2}-a\times 6.

$$\frac{10\left(a-8\right)}{a\left(a-6\right)}+\frac{1}{a-3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a\left(a-6\right) and a-3 is a\left(a-6\right)\left(a-3\right). Multiply \frac{10\left(a-8\right)}{a\left(a-6\right)} times \frac{a-3}{a-3}. Multiply \frac{1}{a-3} times \frac{a\left(a-6\right)}{a\left(a-6\right)}.

$$\frac{10\left(a-8\right)\left(a-3\right)}{a\left(a-6\right)\left(a-3\right)}+\frac{a\left(a-6\right)}{a\left(a-6\right)\left(a-3\right)}$$

Since \frac{10\left(a-8\right)\left(a-3\right)}{a\left(a-6\right)\left(a-3\right)} and \frac{a\left(a-6\right)}{a\left(a-6\right)\left(a-3\right)} have the same denominator, add them by adding their numerators.

$$\frac{10\left(a-8\right)\left(a-3\right)+a\left(a-6\right)}{a\left(a-6\right)\left(a-3\right)}$$

Do the multiplications in 10\left(a-8\right)\left(a-3\right)+a\left(a-6\right).

$$\frac{10a^{2}-30a-80a+240+a^{2}-6a}{a\left(a-6\right)\left(a-3\right)}$$

Combine like terms in 10a^{2}-30a-80a+240+a^{2}-6a.

$$\frac{11a^{2}-116a+240}{a\left(a-6\right)\left(a-3\right)}$$

Expand a\left(a-6\right)\left(a-3\right).

$$\frac{11a^{2}-116a+240}{a^{3}-9a^{2}+18a}$$