Find the Roots (Zeros) F(x)=((x-1)(x+1))/(6(x-4)(x+7))

$F (x) = \frac{(x - 1) (x + 1)}{6 (x - 4) (x + 7)}$

Step 1

Set $\frac{(x - 1) (x + 1)}{6 (x - 4) (x + 7)}$ equal to $0$ .

$\frac{(x - 1) (x + 1)}{6 (x - 4) (x + 7)} = 0$

Step 2

Solve for $x$ .

Set the numerator equal to zero.

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

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 $0$ .

$x - 1 = 0$

$x + 1 = 0$

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.

$x = 1$

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

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

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

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

$x = 1, - 1$

Step 3