Find Where Undefined/Discontinuous y=(3x(x+2))/(x(x+2))

$y = \frac{3 x (x + 2)}{x (x + 2)}$

Step 1

Set the denominator in $\frac{3 x (x + 2)}{x (x + 2)}$ equal to $0$ to find where the expression is undefined.

$x (x + 2) = 0$

Step 2

Solve for $x$ .

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x + 2 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

The final solution is all the values that make $x (x + 2) = 0$ true.

$x = 0, - 2$

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 $0$ .

$x = - 2, x = 0$

Step 4

Find Where Undefined/Discontinuous y=(3x(x+2))/(x(x+2))

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