Find Where Undefined/Discontinuous (3x)/(2x^2+11x-6)

$\frac{3 x}{2 x^{2} + 11 x - 6}$

Step 1

Set the denominator in $\frac{3 x}{2 x^{2} + 11 x - 6}$ equal to $0$ to find where the expression is undefined.

$2 x^{2} + 11 x - 6 = 0$

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 $a \cdot c = 2 \cdot - 6 = - 12$ and whose sum is $b = 11$ .

Factor $11$ out of $11 x$ .

$2 x^{2} + 11 (x) - 6 = 0$

Rewrite $11$ as $- 1$ plus $12$

$2 x^{2} + (- 1 + 12) x - 6 = 0$

Apply the distributive property.

$2 x^{2} - 1 x + 12 x - 6 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 1 x) + 12 x - 6 = 0$

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

$x (2 x - 1) + 6 (2 x - 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x - 1$ .

$(2 x - 1) (x + 6) = 0$

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

$2 x - 1 = 0$

$x + 6 = 0$

Set $2 x - 1$ equal to $0$ and solve for $x$ .

Set $2 x - 1$ equal to $0$ .

$2 x - 1 = 0$

Solve $2 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$2 x = 1$

Divide each term in $2 x = 1$ by $2$ and simplify.

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Divide $x$ by $1$ .

$x = \frac{1}{2}$

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

The final solution is all the values that make $(2 x - 1) (x + 6) = 0$ true.

$x = \frac{1}{2}, - 6$

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 $0$ .

$x = - 6, x = \frac{1}{2}$

Step 4

Find Where Undefined/Discontinuous (3x)/(2x^2+11x-6)

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