Find Where Undefined/Discontinuous (3m^2-2m-35)/(m^2-6m+9)+(m+4)/(m-7)

$\frac{3 m^{2} - 2 m - 35}{m^{2} - 6 m + 9} + \frac{m + 4}{m - 7}$

Step 1

Set the denominator in $\frac{3 m^{2} - 2 m - 35}{m^{2} - 6 m + 9}$ equal to $0$ to find where the expression is undefined.

$m^{2} - 6 m + 9 = 0$

Step 2

Solve for $m$ .

Factor using the perfect square rule.

Rewrite $9$ as $3^{2}$ .

$m^{2} - 6 m + 3^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$6 m = 2 \cdot m \cdot 3$

Rewrite the polynomial.

$m^{2} - 2 \cdot m \cdot 3 + 3^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = m$ and $b = 3$ .

${(m - 3)}^{2} = 0$

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

$m - 3 = 0$

Add $3$ to both sides of the equation.

$m = 3$

Step 3

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

$m - 7 = 0$

Step 4

Add $7$ to both sides of the equation.

$m = 7$

Step 5

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 $0$ .

$m = 3, m = 7$

Step 6

Find Where Undefined/Discontinuous (3m^2-2m-35)/(m^2-6m+9)+(m+4)/(m-7)

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