Simplify (n^2+7n-18)/(n^2-5n+6)-1/(n-3)

$\frac{n^{2} + 7 n - 18}{n^{2} - 5 n + 6} - \frac{1}{n - 3}$

Step 1

Simplify each term.

Factor $n^{2} + 7 n - 18$ 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 $7$ .

$- 2, 9$

Write the factored form using these integers.

$\frac{(n - 2) (n + 9)}{n^{2} - 5 n + 6} - \frac{1}{n - 3}$

Factor $n^{2} - 5 n + 6$ 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 $6$ and whose sum is $- 5$ .

$- 3, - 2$

Write the factored form using these integers.

$\frac{(n - 2) (n + 9)}{(n - 3) (n - 2)} - \frac{1}{n - 3}$

Cancel the common factor of $n - 2$ .

Cancel the common factor.

$\frac{(n - 2) (n + 9)}{(n - 3) (n - 2)} - \frac{1}{n - 3}$

Rewrite the expression.

$\frac{n + 9}{n - 3} - \frac{1}{n - 3}$

Step 2

Combine fractions.

Combine the numerators over the common denominator.

$\frac{n + 9 - 1}{n - 3}$

Subtract $1$ from $9$ .

$\frac{n + 8}{n - 3}$

Simplify (n^2+7n-18)/(n^2-5n+6)-1/(n-3)

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