Find Where Undefined/Discontinuous (27-3x^2)/(7x^2-63)

$\frac{27 - 3 x^{2}}{7 x^{2} - 63}$

Step 1

Set the denominator in $\frac{27 - 3 x^{2}}{7 x^{2} - 63}$ equal to $0$ to find where the expression is undefined.

$7 x^{2} - 63 = 0$

Step 2

Solve for $x$ .

Add $63$ to both sides of the equation.

$7 x^{2} = 63$

Divide each term in $7 x^{2} = 63$ by $7$ and simplify.

Divide each term in $7 x^{2} = 63$ by $7$ .

$\frac{7 x^{2}}{7} = \frac{63}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x^{2}}{7} = \frac{63}{7}$

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

$x^{2} = \frac{63}{7}$

Simplify the right side.

Divide $63$ by $7$ .

$x^{2} = 9$

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

$x = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

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

$x = \pm \sqrt{3^{2}}$

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

$x = \pm 3$

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.

$x = 3$

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

$x = - 3$

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

$x = 3, - 3$

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 $0$ .

$x = - 3, x = 3$

Step 4

Find Where Undefined/Discontinuous (27-3x^2)/(7x^2-63)

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