Find the Roots (Zeros) F(x)=(x(x-2))/((x+3)(x-5))

$F (x) = \frac{x (x - 2)}{(x + 3) (x - 5)}$

Step 1

Set $\frac{x (x - 2)}{(x + 3) (x - 5)}$ equal to $0$ .

$\frac{x (x - 2)}{(x + 3) (x - 5)} = 0$

Step 2

Solve for $x$ .

Set the numerator equal to zero.

$x (x - 2) = 0$

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 $0$ .

$x = 0$

$x - 2 = 0$

Set $x$ equal to $0$ .

$x = 0$

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

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

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

$x = 0, 2$

Step 3