Calculus Examples

$\frac{x + 1}{x^{2} - 4 x - 5}$

Step 1

Write $\frac{x + 1}{x^{2} - 4 x - 5}$ as an equation.

$y = \frac{x + 1}{x^{2} - 4 x - 5}$

Step 2

Find the x-intercepts.

Tap for more steps...

Step 2.1

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

$0 = \frac{x + 1}{x^{2} - 4 x - 5}$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Set the numerator equal to zero.

$x + 1 = 0$

Step 2.2.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 2.2.3

Exclude the solutions that do not make $0 = \frac{x + 1}{x^{2} - 4 x - 5}$ true.

$No solution$

Step 2.3

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

x-intercept(s): $None$

Step 3

Find the y-intercepts.

Tap for more steps...

Step 3.1

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

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

Step 3.2

Solve the equation.

Tap for more steps...

Step 3.2.1

Remove parentheses.

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

Step 3.2.2

Remove parentheses.

$y = \frac{0 + 1}{0^{2} - 4 \cdot 0 - 5}$

Step 3.2.3

Remove parentheses.

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

Step 3.2.4

Simplify $\frac{(0) + 1}{{(0)}^{2} - 4 \cdot 0 - 5}$ .

Tap for more steps...

Step 3.2.4.1

Add $0$ and $1$ .

$y = \frac{1}{0^{2} - 4 \cdot 0 - 5}$

Step 3.2.4.2

Simplify the denominator.

Tap for more steps...

Step 3.2.4.2.1

Raising $0$ to any positive power yields $0$ .

$y = \frac{1}{0 - 4 \cdot 0 - 5}$

Step 3.2.4.2.2

Multiply $- 4$ by $0$ .

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

Step 3.2.4.2.3

Add $0$ and $0$ .

$y = \frac{1}{0 - 5}$

Step 3.2.4.2.4

Subtract $5$ from $0$ .

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

Step 3.2.4.3

Move the negative in front of the fraction.

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

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{1}{5})$

Step 4

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - \frac{1}{5})$

Step 5