Calculus Examples

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

Step 1

Set $- \frac{2 {(x - 2)}^{2}}{{(x (x - 2))}^{2}}$ equal to $0$ .

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

Step 2

Solve for $x$ .

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Step 2.1

Set the numerator equal to zero.

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

Step 2.2

Solve the equation for $x$ .

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Step 2.2.1

Divide each term in $2 {(x - 2)}^{2} = 0$ by $2$ and simplify.

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Step 2.2.1.1

Divide each term in $2 {(x - 2)}^{2} = 0$ by $2$ .

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

Step 2.2.1.2

Simplify the left side.

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Step 2.2.1.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.2.1.1

Cancel the common factor.

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

Step 2.2.1.2.1.2

Divide ${(x - 2)}^{2}$ by $1$ .

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

Step 2.2.1.3

Simplify the right side.

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Step 2.2.1.3.1

Divide $0$ by $2$ .

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

Step 2.2.2

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

$x - 2 = 0$

Step 2.2.3

Add $2$ to both sides of the equation.

$x = 2$

Step 2.3

Exclude the solutions that do not make $- \frac{2 {(x - 2)}^{2}}{{(x (x - 2))}^{2}} = 0$ true.

$No solution$