Simplify (3a)/(a^2-9a+18)-2/(a-6)

$\frac{3 a}{a^{2} - 9 a + 18} - \frac{2}{a - 6}$

Factor $a^{2} - 9 a + 18$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $18$ and whose sum is $- 9$ .

$- 6, - 3$

Write the factored form using these integers.

$\frac{3 a}{(a - 6) (a - 3)} - \frac{2}{a - 6}$

To write $- \frac{2}{a - 6}$ as a fraction with a common denominator, multiply by $\frac{a - 3}{a - 3}$ .

$\frac{3 a}{(a - 6) (a - 3)} - \frac{2}{a - 6} \cdot \frac{a - 3}{a - 3}$

Simplify terms.

Multiply $\frac{2}{a - 6}$ by $\frac{a - 3}{a - 3}$ .

$\frac{3 a}{(a - 6) (a - 3)} - \frac{2 (a - 3)}{(a - 6) (a - 3)}$

Combine the numerators over the common denominator.

$\frac{3 a - 2 (a - 3)}{(a - 6) (a - 3)}$

Simplify the numerator.

Apply the distributive property.

$\frac{3 a - 2 a - 2 \cdot - 3}{(a - 6) (a - 3)}$

Multiply $- 2$ by $- 3$ .

$\frac{3 a - 2 a + 6}{(a - 6) (a - 3)}$

Subtract $2 a$ from $3 a$ .

$\frac{a + 6}{(a - 6) (a - 3)}$

Simplify (3a)/(a^2-9a+18)-2/(a-6)

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