Calculus Examples

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

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

Step 1

Set

- \frac{2 {(x - 2)}^{2}}{{(x (x - 2))}^{2}}

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

0

$0$ .

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

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

Step 2

Solve for

x

$x$ .

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Step 2.1

Set the numerator equal to zero.

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

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

Step 2.2

Solve the equation for

x

$x$ .

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Step 2.2.1

Divide each term in

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

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

2

$2$ and simplify.

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Step 2.2.1.1

Divide each term in

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

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

2

$2$ .

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

$2$ .

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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.

$No solution$