Algebra Examples

$\frac{(x - 4) (x + 2)}{(x - 4) (x + 1)}$

Step 1

Set $\frac{(x - 4) (x + 2)}{(x - 4) (x + 1)}$ equal to $0$ .

$\frac{(x - 4) (x + 2)}{(x - 4) (x + 1)} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Set the numerator equal to zero.

$(x - 4) (x + 2) = 0$

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 $0$ .

$x - 4 = 0$

$x + 2 = 0$

Step 2.2.2

Set $x - 4$ equal to $0$ and solve for $x$ .

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Step 2.2.2.1

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Step 2.2.2.2

Add $4$ to both sides of the equation.

$x = 4$

Step 2.2.3

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

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Step 2.2.3.1

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

$x + 2 = 0$

Step 2.2.3.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 2.2.4

The final solution is all the values that make $(x - 4) (x + 2) = 0$ true.

$x = 4, - 2$

Step 2.3

Exclude the solutions that do not make $\frac{(x - 4) (x + 2)}{(x - 4) (x + 1)} = 0$ true.

$x = - 2$

Step 3