Algebra Examples

$f (x) = \frac{(3 x + 4) (x + 2)}{(x - 4) (x + 2)}$

Step 1

Set $\frac{(3 x + 4) (x + 2)}{(x - 4) (x + 2)}$ equal to $0$ .

$\frac{(3 x + 4) (x + 2)}{(x - 4) (x + 2)} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Set the numerator equal to zero.

$(3 x + 4) (x + 2) = 0$

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 $0$ .

$3 x + 4 = 0$

$x + 2 = 0$

Step 2.2.2

Set $3 x + 4$ equal to $0$ and solve for $x$ .

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Step 2.2.2.1

Set $3 x + 4$ equal to $0$ .

$3 x + 4 = 0$

Step 2.2.2.2

Solve $3 x + 4 = 0$ for $x$ .

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Step 2.2.2.2.1

Subtract $4$ from both sides of the equation.

$3 x = - 4$

Step 2.2.2.2.2

Divide each term in $3 x = - 4$ by $3$ and simplify.

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Step 2.2.2.2.2.1

Divide each term in $3 x = - 4$ by $3$ .

$\frac{3 x}{3} = \frac{- 4}{3}$

Step 2.2.2.2.2.2

Simplify the left side.

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Step 2.2.2.2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 4}{3}$

Step 2.2.2.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{3}$

Step 2.2.2.2.2.3

Simplify the right side.

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Step 2.2.2.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

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 $(3 x + 4) (x + 2) = 0$ true.

$x = - \frac{4}{3}, - 2$

Step 2.3

Exclude the solutions that do not make $\frac{(3 x + 4) (x + 2)}{(x - 4) (x + 2)} = 0$ true.

$x = - \frac{4}{3}$

Step 3