Find the Excluded Values (4m^2-14m+12)/(12m^2-27)

$\frac{4 m^{2} - 14 m + 12}{12 m^{2} - 27}$

Set the denominator in $\frac{4 m^{2} - 14 m + 12}{12 m^{2} - 27}$ equal to $0$ to find where the expression is undefined.

$12 m^{2} - 27 = 0$

Solve for $m$ .

Add $27$ to both sides of the equation.

$12 m^{2} = 27$

Divide each term in $12 m^{2} = 27$ by $12$ and simplify.

Divide each term in $12 m^{2} = 27$ by $12$ .

$\frac{12 m^{2}}{12} = \frac{27}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 m^{2}}{12} = \frac{27}{12}$

Divide $m^{2}$ by $1$ .

$m^{2} = \frac{27}{12}$

Simplify the right side.

Cancel the common factor of $27$ and $12$ .

Factor $3$ out of $27$ .

$m^{2} = \frac{3 (9)}{12}$

Cancel the common factors.

Factor $3$ out of $12$ .

$m^{2} = \frac{3 \cdot 9}{3 \cdot 4}$

Cancel the common factor.

$m^{2} = \frac{3 \cdot 9}{3 \cdot 4}$

Rewrite the expression.

$m^{2} = \frac{9}{4}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$m = \pm \sqrt{\frac{9}{4}}$

Simplify $\pm \sqrt{\frac{9}{4}}$ .

Rewrite $\sqrt{\frac{9}{4}}$ as $\frac{\sqrt{9}}{\sqrt{4}}$ .

$m = \pm \frac{\sqrt{9}}{\sqrt{4}}$

Simplify the numerator.

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

$m = \pm \frac{\sqrt{3^{2}}}{\sqrt{4}}$

Pull terms out from under the radical, assuming positive real numbers.

$m = \pm \frac{3}{\sqrt{4}}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$m = \pm \frac{3}{\sqrt{2^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$m = \pm \frac{3}{2}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$m = \frac{3}{2}$

Next, use the negative value of the $\pm$ to find the second solution.

$m = - \frac{3}{2}$

The complete solution is the result of both the positive and negative portions of the solution.

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

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 $0$ .

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

Find the Excluded Values (4m^2-14m+12)/(12m^2-27)

Related Questions

Support LCMGCF.com by disabling your adblocker.