Find the Roots (Zeros) ((x-1)(x+5))/(x-5)

$\frac{(x - 1) (x + 5)}{x - 5}$

Step 1

Set $\frac{(x - 1) (x + 5)}{x - 5}$ equal to $0$ .

$\frac{(x - 1) (x + 5)}{x - 5} = 0$

Step 2

Solve for $x$ .

Set the numerator equal to zero.

$(x - 1) (x + 5) = 0$

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 $0$ .

$x - 1 = 0$

$x + 5 = 0$

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 $x + 5$ equal to $0$ and solve for $x$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

The final solution is all the values that make $(x - 1) (x + 5) = 0$ true.

$x = 1, - 5$

Step 3