Find Where Undefined/Discontinuous 13/(3x^2-14x-80)

$\frac{13}{3 x^{2} - 14 x - 80}$

Step 1

Set the denominator in $\frac{13}{3 x^{2} - 14 x - 80}$ equal to $0$ to find where the expression is undefined.

$3 x^{2} - 14 x - 80 = 0$

Step 2

Solve for $x$ .

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot - 80 = - 240$ and whose sum is $b = - 14$ .

Factor $- 14$ out of $- 14 x$ .

$3 x^{2} - 14 x - 80 = 0$

Rewrite $- 14$ as $10$ plus $- 24$

$3 x^{2} + (10 - 24) x - 80 = 0$

Apply the distributive property.

$3 x^{2} + 10 x - 24 x - 80 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} + 10 x) - 24 x - 80 = 0$

Factor out the greatest common factor (GCF) from each group.

$x (3 x + 10) - 8 (3 x + 10) = 0$

Factor the polynomial by factoring out the greatest common factor, $3 x + 10$ .

$(3 x + 10) (x - 8) = 0$

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

$3 x + 10 = 0$

$x - 8 = 0$

Set $3 x + 10$ equal to $0$ and solve for $x$ .

Set $3 x + 10$ equal to $0$ .

$3 x + 10 = 0$

Solve $3 x + 10 = 0$ for $x$ .

Subtract $10$ from both sides of the equation.

$3 x = - 10$

Divide each term in $3 x = - 10$ by $3$ and simplify.

Divide each term in $3 x = - 10$ by $3$ .

$\frac{3 x}{3} = \frac{- 10}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 10}{3}$

Divide $x$ by $1$ .

$x = \frac{- 10}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{10}{3}$

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

The final solution is all the values that make $(3 x + 10) (x - 8) = 0$ true.

$x = - \frac{10}{3}, 8$

Step 3

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 $0$ .

$x = - \frac{10}{3}, x = 8$

Step 4

Find Where Undefined/Discontinuous 13/(3x^2-14x-80)

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