Find the Roots (Zeros) F(x)=((x+3)(x-1))/((x-2)(x+2))

$F (x) = \frac{(x + 3) (x - 1)}{(x - 2) (x + 2)}$

Step 1

Set $\frac{(x + 3) (x - 1)}{(x - 2) (x + 2)}$ equal to $0$ .

$\frac{(x + 3) (x - 1)}{(x - 2) (x + 2)} = 0$

Step 2

Solve for $x$ .

Set the numerator equal to zero.

$(x + 3) (x - 1) = 0$

Solve the equation for $x$ .

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

$x + 3 = 0$

$x - 1 = 0$

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

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

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

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

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

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The final solution is all the values that make $(x + 3) (x - 1) = 0$ true.

$x = - 3, 1$

Step 3