Find Where Undefined/Discontinuous (x^2-26x+169)/(1859-11x^2)

$\frac{x^{2} - 26 x + 169}{1859 - 11 x^{2}}$

Step 1

Set the denominator in $\frac{x^{2} - 26 x + 169}{1859 - 11 x^{2}}$ equal to $0$ to find where the expression is undefined.

$1859 - 11 x^{2} = 0$

Step 2

Solve for $x$ .

Subtract $1859$ from both sides of the equation.

$- 11 x^{2} = - 1859$

Divide each term in $- 11 x^{2} = - 1859$ by $- 11$ and simplify.

Divide each term in $- 11 x^{2} = - 1859$ by $- 11$ .

$\frac{- 11 x^{2}}{- 11} = \frac{- 1859}{- 11}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 x^{2}}{- 11} = \frac{- 1859}{- 11}$

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

$x^{2} = \frac{- 1859}{- 11}$

Simplify the right side.

Divide $- 1859$ by $- 11$ .

$x^{2} = 169$

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

$x = \pm \sqrt{169}$

Simplify $\pm \sqrt{169}$ .

Rewrite $169$ as $13^{2}$ .

$x = \pm \sqrt{13^{2}}$

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

$x = \pm 13$

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.

$x = 13$

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

$x = - 13$

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

$x = 13, - 13$

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 $0$ .

$x = - 13, x = 13$

Step 4

Find Where Undefined/Discontinuous (x^2-26x+169)/(1859-11x^2)

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