Find Where Undefined/Discontinuous (x^2+5x-36)/(x^2-49)*(x^2-11x+28)

$\frac{x^{2} + 5 x - 36}{x^{2} - 49} \cdot (x^{2} - 11 x + 28)$

Step 1

Set the denominator in $\frac{x^{2} + 5 x - 36}{x^{2} - 49}$ equal to $0$ to find where the expression is undefined.

$x^{2} - 49 = 0$

Step 2

Solve for $x$ .

Add $49$ to both sides of the equation.

$x^{2} = 49$

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

$x = \pm \sqrt{49}$

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$x = \pm \sqrt{7^{2}}$

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

$x = \pm 7$

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.

$x = 7$

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

$x = - 7$

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

$x = 7, - 7$

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 $0$ .

$x = - 7, x = 7$

Step 4

Find Where Undefined/Discontinuous (x^2+5x-36)/(x^2-49)*(x^2-11x+28)

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