Question

1. find the values of x for which the denominator is equal to zero for $y = \frac{2x^2 + 5}{x^2 - 2x}$

options:
$x = 1, x = 2$
none
$x = 2$
$x = 0, x = 2$

Explanation:

Step1: Identify the denominator

The denominator is $x^2 - 2x$.

Step2: Set denominator to zero

Solve $x^2 - 2x = 0$.

Step3: Factor the equation

$x(x - 2) = 0$.

Step4: Find roots

$x=0$ or $x=2$. But wait—check the original problem's options: the first option is "x=0,x=2" (assuming the last option is this, as per common formatting). Wait no, looking at the image options: the options are likely (from right to left? No, standard order: first option is "x=1,x=2", second "none", third "x=2", fourth "x=0,x=2"). Wait no, the problem says "find x where denominator is zero"—denominator $x²-2x=0$ → $x=0$ or $x=2$. If one of the options is "x=0,x=2", that's the answer. But if the options are as listed in the image (the last option is "x=0,x=2"), then that's the answer. Wait, correcting: the denominator is $x² - 2x$, so $x(x-2)=0$ → $x=0$ or $x=2$. So the correct option is the one with $x=0,x=2$.

Wait, adjusting to match the image's options (the fourth option from the right is "x=0,x=2"):

Step1: Locate the denominator

Denominator: $x^2 - 2x$.

Step2: Solve denominator = 0

$x^2 - 2x = 0$.

Step3: Factor the expression

$x(x - 2) = 0$.

Step4: Determine roots

$x=0$ or $x=2$.

Answer:

none