Find Where Undefined/Discontinuous y=5/((x+1)^2-1)

$y = \frac{5}{{(x + 1)}^{2} - 1}$

Set the denominator in $\frac{5}{{(x + 1)}^{2} - 1}$ equal to $0$ to find where the expression is undefined.

${(x + 1)}^{2} - 1 = 0$

Solve for $x$ .

Add $1$ to both sides of the equation.

${(x + 1)}^{2} = 1$

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

$x + 1 = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$x + 1 = \pm 1$

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.

$x + 1 = 1$

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$x = 1 - 1$

Subtract $1$ from $1$ .

$x = 0$

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

$x + 1 = - 1$

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$x = - 1 - 1$

Subtract $1$ from $- 1$ .

$x = - 2$

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

$x = 0, - 2$

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 $0$ .

$x = - 2, x = 0$

Find Where Undefined/Discontinuous y=5/((x+1)^2-1)

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