Find Where Undefined/Discontinuous (-8m^2+8m-2)/(32m^2-4m-6)

$\frac{- 8 m^{2} + 8 m - 2}{32 m^{2} - 4 m - 6}$

Step 1

Set the denominator in $\frac{- 8 m^{2} + 8 m - 2}{32 m^{2} - 4 m - 6}$ equal to $0$ to find where the expression is undefined.

$32 m^{2} - 4 m - 6 = 0$

Step 2

Solve for $m$ .

Factor the left side of the equation.

Factor $2$ out of $32 m^{2} - 4 m - 6$ .

Factor $2$ out of $32 m^{2}$ .

$2 (16 m^{2}) - 4 m - 6 = 0$

Factor $2$ out of $- 4 m$ .

$2 (16 m^{2}) + 2 (- 2 m) - 6 = 0$

Factor $2$ out of $- 6$ .

$2 (16 m^{2}) + 2 (- 2 m) + 2 (- 3) = 0$

Factor $2$ out of $2 (16 m^{2}) + 2 (- 2 m)$ .

$2 (16 m^{2} - 2 m) + 2 (- 3) = 0$

Factor $2$ out of $2 (16 m^{2} - 2 m) + 2 (- 3)$ .

$2 (16 m^{2} - 2 m - 3) = 0$

Factor.

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 $a \cdot c = 16 \cdot - 3 = - 48$ and whose sum is $b = - 2$ .

Factor $- 2$ out of $- 2 m$ .

$2 (16 m^{2} - 2 m - 3) = 0$

Rewrite $- 2$ as $6$ plus $- 8$

$2 (16 m^{2} + (6 - 8) m - 3) = 0$

Apply the distributive property.

$2 (16 m^{2} + 6 m - 8 m - 3) = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((16 m^{2} + 6 m) - 8 m - 3) = 0$

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

$2 (2 m (8 m + 3) - (8 m + 3)) = 0$

Factor the polynomial by factoring out the greatest common factor, $8 m + 3$ .

$2 ((8 m + 3) (2 m - 1)) = 0$

Remove unnecessary parentheses.

$2 (8 m + 3) (2 m - 1) = 0$

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

$8 m + 3 = 0$

$2 m - 1 = 0$

Set $8 m + 3$ equal to $0$ and solve for $m$ .

Set $8 m + 3$ equal to $0$ .

$8 m + 3 = 0$

Solve $8 m + 3 = 0$ for $m$ .

Subtract $3$ from both sides of the equation.

$8 m = - 3$

Divide each term in $8 m = - 3$ by $8$ and simplify.

Divide each term in $8 m = - 3$ by $8$ .

$\frac{8 m}{8} = \frac{- 3}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 m}{8} = \frac{- 3}{8}$

Divide $m$ by $1$ .

$m = \frac{- 3}{8}$

Simplify the right side.

Move the negative in front of the fraction.

$m = - \frac{3}{8}$

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

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

$2 m - 1 = 0$

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

Add $1$ to both sides of the equation.

$2 m = 1$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $m$ by $1$ .

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

The final solution is all the values that make $2 (8 m + 3) (2 m - 1) = 0$ true.

$m = - \frac{3}{8}, \frac{1}{2}$

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 $0$ .

$m = - \frac{3}{8}, m = \frac{1}{2}$

Step 4

Find Where Undefined/Discontinuous (-8m^2+8m-2)/(32m^2-4m-6)

Related Questions

Support LCMGCF.com by disabling your adblocker.