Precalculus Examples

$\frac{x + 1}{x^{2} + 2 x - 3}$

Step 1

Write $\frac{x + 1}{x^{2} + 2 x - 3}$ as an equation.

$y = \frac{x + 1}{x^{2} + 2 x - 3}$

Step 2

Find the x-intercepts.

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Step 2.1

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

$0 = \frac{x + 1}{x^{2} + 2 x - 3}$

Step 2.2

Solve the equation.

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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 2.3

x-intercept(s) in point form.

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

Step 3

Find the y-intercepts.

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Step 3.1

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

$y = \frac{(0) + 1}{{(0)}^{2} + 2 (0) - 3}$

Step 3.2

Solve the equation.

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Step 3.2.1

Remove parentheses.

$y = \frac{0 + 1}{{(0)}^{2} + 2 (0) - 3}$

Step 3.2.2

Remove parentheses.

$y = \frac{0 + 1}{0^{2} + 2 (0) - 3}$

Step 3.2.3

Remove parentheses.

$y = \frac{(0) + 1}{{(0)}^{2} + 2 (0) - 3}$

Step 3.2.4

Simplify $\frac{(0) + 1}{{(0)}^{2} + 2 (0) - 3}$ .

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Step 3.2.4.1

Add $0$ and $1$ .

$y = \frac{1}{0^{2} + 2 (0) - 3}$

Step 3.2.4.2

Simplify the denominator.

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Step 3.2.4.2.1

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

$y = \frac{1}{0 + 2 (0) - 3}$

Step 3.2.4.2.2

Multiply $2$ by $0$ .

$y = \frac{1}{0 + 0 - 3}$

Step 3.2.4.2.3

Add $0$ and $0$ .

$y = \frac{1}{0 - 3}$

Step 3.2.4.2.4

Subtract $3$ from $0$ .

$y = \frac{1}{- 3}$

Step 3.2.4.3

Move the negative in front of the fraction.

$y = - \frac{1}{3}$

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{1}{3})$

Step 4

List the intersections.

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

y-intercept(s): $(0, - \frac{1}{3})$

Step 5