Find the x and y Intercepts h(x)=((x-1)(x-5))/((2x)(x-4))

$h (x) = \frac{(x - 1) (x - 5)}{(2 x) (x - 4)}$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{(x - 1) (x - 5)}{(2 x) (x - 4)}$

Solve the equation.

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 $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

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

$x = 1, 5$

x-intercept(s) in point form.

x-intercept(s): $(1, 0), (5, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{((0) - 1) ((0) - 5)}{(2 (0)) ((0) - 4)}$

The equation has an undefined fraction.

Undefined

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

y-intercept(s): $None$

Step 3

List the intersections.

x-intercept(s): $(1, 0), (5, 0)$

y-intercept(s): $None$

Step 4