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

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

Step 1

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

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

Step 2

Solve for $x$ .

Factor $x$ out of $x^{2} - 2 x$ .

Factor $x$ out of $x^{2}$ .

$x \cdot x - 2 x = 0$

Factor $x$ out of $- 2 x$ .

$x \cdot x + x \cdot - 2 = 0$

Factor $x$ out of $x \cdot x + x \cdot - 2$ .

$x (x - 2) = 0$

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 $0$ .

$x - 2 = 0$

Add $2$ to 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 $0$ .

$x = 0, x = 2$

Step 4

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

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