Find the x and y Intercepts (x^2+4x-45)/(x^2-9)

$\frac{x^{2} + 4 x - 45}{x^{2} - 9}$

Step 1

Write $\frac{x^{2} + 4 x - 45}{x^{2} - 9}$ as an equation.

$y = \frac{x^{2} + 4 x - 45}{x^{2} - 9}$

Step 2

Find the x-intercepts.

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

$0 = \frac{x^{2} + 4 x - 45}{x^{2} - 9}$

Solve the equation.

Set the numerator equal to zero.

$x^{2} + 4 x - 45 = 0$

Solve the equation for $x$ .

Factor $x^{2} + 4 x - 45$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 45$ and whose sum is $4$ .

$- 5, 9$

Write the factored form using these integers.

$(x - 5) (x + 9) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 5 = 0$

$x + 9 = 0$

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.

$x = 5$

Set $x + 9$ equal to $0$ and solve for $x$ .

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Subtract $9$ from both sides of the equation.

$x = - 9$

The final solution is all the values that make $(x - 5) (x + 9) = 0$ true.

$x = 5, - 9$

x-intercept(s) in point form.

x-intercept(s): $(5, 0), (- 9, 0)$

Step 3

Find the y-intercepts.

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

$y = \frac{{(0)}^{2} + 4 (0) - 45}{{(0)}^{2} - 9}$

Solve the equation.

Remove parentheses.

$y = \frac{0^{2} + 4 (0) - 45}{{(0)}^{2} - 9}$

Remove parentheses.

$y = \frac{0^{2} + 4 (0) - 45}{0^{2} - 9}$

Remove parentheses.

$y = \frac{{(0)}^{2} + 4 (0) - 45}{{(0)}^{2} - 9}$

Simplify $\frac{{(0)}^{2} + 4 (0) - 45}{{(0)}^{2} - 9}$ .

Simplify the numerator.

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

$y = \frac{0 + 4 (0) - 45}{0^{2} - 9}$

Multiply $4$ by $0$ .

$y = \frac{0 + 0 - 45}{0^{2} - 9}$

Add $0$ and $0$ .

$y = \frac{0 - 45}{0^{2} - 9}$

Subtract $45$ from $0$ .

$y = \frac{- 45}{0^{2} - 9}$

Simplify the denominator.

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

$y = \frac{- 45}{0 - 9}$

Subtract $9$ from $0$ .

$y = \frac{- 45}{- 9}$

Divide $- 45$ by $- 9$ .

$y = 5$

y-intercept(s) in point form.

y-intercept(s): $(0, 5)$

Step 4

List the intersections.

x-intercept(s): $(5, 0), (- 9, 0)$

y-intercept(s): $(0, 5)$

Step 5

Find the x and y Intercepts (x^2+4x-45)/(x^2-9)

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