Find the Excluded Values (p^2-3p-10)/(p^2+p-2)

$\frac{p^{2} - 3 p - 10}{p^{2} + p - 2}$

Set the denominator in $\frac{p^{2} - 3 p - 10}{p^{2} + p - 2}$ equal to $0$ to find where the expression is undefined.

$p^{2} + p - 2 = 0$

Solve for $p$ .

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

$- 1, 2$

Write the factored form using these integers.

$(p - 1) (p + 2) = 0$

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

$p - 1 = 0$

$p + 2 = 0$

Set $p - 1$ equal to $0$ and solve for $p$ .

Set $p - 1$ equal to $0$ .

$p - 1 = 0$

Add $1$ to both sides of the equation.

$p = 1$

Set $p + 2$ equal to $0$ and solve for $p$ .

Set $p + 2$ equal to $0$ .

$p + 2 = 0$

Subtract $2$ from both sides of the equation.

$p = - 2$

The final solution is all the values that make $(p - 1) (p + 2) = 0$ true.

$p = 1, - 2$

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 $0$ .

$p = - 2, p = 1$

Find the Excluded Values (p^2-3p-10)/(p^2+p-2)

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