Find the Excluded Values (m+7)/(m^2+4m-21)

$\frac{m + 7}{m^{2} + 4 m - 21}$

Set the denominator in $\frac{m + 7}{m^{2} + 4 m - 21}$ equal to $0$ to find where the expression is undefined.

$m^{2} + 4 m - 21 = 0$

Solve for $m$ .

Factor $m^{2} + 4 m - 21$ 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 $- 21$ and whose sum is $4$ .

$- 3, 7$

Write the factored form using these integers.

$(m - 3) (m + 7) = 0$

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

$m - 3 = 0$

$m + 7 = 0$

Set $m - 3$ equal to $0$ and solve for $m$ .

Set $m - 3$ equal to $0$ .

$m - 3 = 0$

Add $3$ to both sides of the equation.

$m = 3$

Set $m + 7$ equal to $0$ and solve for $m$ .

Set $m + 7$ equal to $0$ .

$m + 7 = 0$

Subtract $7$ from both sides of the equation.

$m = - 7$

The final solution is all the values that make $(m - 3) (m + 7) = 0$ true.

$m = 3, - 7$

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 $0$ .

$m = - 7, m = 3$

Find the Excluded Values (m+7)/(m^2+4m-21)

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