Algebra Examples

$F (x) = \frac{x (x - 1) (x + 11)}{(x + 12) (x - 13)}$

Step 1

Set $\frac{x (x - 1) (x + 11)}{(x + 12) (x - 13)}$ equal to $0$ .

$\frac{x (x - 1) (x + 11)}{(x + 12) (x - 13)} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Set the numerator equal to zero.

$x (x - 1) (x + 11) = 0$

Step 2.2

Solve the equation for $x$ .

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Step 2.2.1

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

$x = 0$

$x - 1 = 0$

$x + 11 = 0$

Step 2.2.2

Set $x$ equal to $0$ .

$x = 0$

Step 2.2.3

Set $x - 1$ equal to $0$ and solve for $x$ .

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Step 2.2.3.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 2.2.3.2

Add $1$ to both sides of the equation.

$x = 1$

Step 2.2.4

Set $x + 11$ equal to $0$ and solve for $x$ .

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Step 2.2.4.1

Set $x + 11$ equal to $0$ .

$x + 11 = 0$

Step 2.2.4.2

Subtract $11$ from both sides of the equation.

$x = - 11$

Step 2.2.5

The final solution is all the values that make $x (x - 1) (x + 11) = 0$ true.

$x = 0, 1, - 11$

Step 3