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

$y = \frac{(x + 1)}{(x + 2) (x - 5)}$

Step 1

Find the x-intercepts.

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

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

Solve the equation.

Set the numerator equal to zero.

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

Simplify $\frac{(0) + 1}{((0) + 2) ((0) - 5)}$ .

Add $0$ and $1$ .

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

Simplify the denominator.

Add $0$ and $2$ .

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

Subtract $5$ from $0$ .

$y = \frac{1}{2 \cdot - 5}$

Simplify the expression.

Multiply $2$ by $- 5$ .

$y = \frac{1}{- 10}$

Move the negative in front of the fraction.

$y = - \frac{1}{10}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{1}{10})$

Step 3

List the intersections.

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

y-intercept(s): $(0, - \frac{1}{10})$

Step 4