Calculus Examples

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

Step 1

Set the numerator equal to zero.

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

Step 2

Solve the equation for $x$ .

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Step 2.1

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

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Step 2.1.1

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

$x \cdot x - 2 x = 0$

Step 2.1.2

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

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

Step 2.1.3

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

$x (x - 2) = 0$

Step 2.2

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

$x = 0$

$x - 2 = 0$

Step 2.3

Set $x$ equal to $0$ .

$x = 0$

Step 2.4

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

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Step 2.4.1

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

$x - 2 = 0$

Step 2.4.2

Add $2$ to both sides of the equation.

$x = 2$

Step 2.5

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

$x = 0, 2$