Find the Excluded Values (n^2-13n+36)/(n^2+n-90)

$\frac{n^{2} - 13 n + 36}{n^{2} + n - 90}$

Set the denominator in $\frac{n^{2} - 13 n + 36}{n^{2} + n - 90}$ equal to $0$ to find where the expression is undefined.

$n^{2} + n - 90 = 0$

Solve for $n$ .

Factor $n^{2} + n - 90$ 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 $- 90$ and whose sum is $1$ .

$- 9, 10$

Write the factored form using these integers.

$(n - 9) (n + 10) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$n - 9 = 0$

$n + 10 = 0$

Set $n - 9$ equal to $0$ and solve for $n$ .

Set $n - 9$ equal to $0$ .

$n - 9 = 0$

Add $9$ to both sides of the equation.

$n = 9$

Set $n + 10$ equal to $0$ and solve for $n$ .

Set $n + 10$ equal to $0$ .

$n + 10 = 0$

Subtract $10$ from both sides of the equation.

$n = - 10$

The final solution is all the values that make $(n - 9) (n + 10) = 0$ true.

$n = 9, - 10$

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$n = - 10, n = 9$

Find the Excluded Values (n^2-13n+36)/(n^2+n-90)

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