Find the x and y Intercepts (5x^2-5)/(-3x^2-6x+9)

$\frac{5 x^{2} - 5}{- 3 x^{2} - 6 x + 9}$

Write $\frac{5 x^{2} - 5}{- 3 x^{2} - 6 x + 9}$ as an equation.

$y = \frac{5 x^{2} - 5}{- 3 x^{2} - 6 x + 9}$

Find the x-intercepts.

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

$0 = \frac{5 x^{2} - 5}{- 3 x^{2} - 6 x + 9}$

Solve the equation.

Set the numerator equal to zero.

$5 x^{2} - 5 = 0$

Solve the equation for $x$ .

Add $5$ to both sides of the equation.

$5 x^{2} = 5$

Divide each term in $5 x^{2} = 5$ by $5$ and simplify.

Divide each term in $5 x^{2} = 5$ by $5$ .

$\frac{5 x^{2}}{5} = \frac{5}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x^{2}}{5} = \frac{5}{5}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{5}{5}$

Simplify the right side.

Divide $5$ by $5$ .

$x^{2} = 1$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$x = \pm 1$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 1$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 1$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 1, - 1$

Exclude the solutions that do not make $0 = \frac{5 x^{2} - 5}{- 3 x^{2} - 6 x + 9}$ true.

$x = - 1$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = \frac{5 {(0)}^{2} - 5}{- 3 {(0)}^{2} - 6 \cdot 0 + 9}$

Solve the equation.

Remove parentheses.

$y = \frac{5 \cdot 0^{2} - 5}{- 3 {(0)}^{2} - 6 \cdot 0 + 9}$

Remove parentheses.

$y = \frac{5 \cdot 0^{2} - 5}{- 3 \cdot 0^{2} - 6 \cdot 0 + 9}$

Remove parentheses.

$y = \frac{5 {(0)}^{2} - 5}{- 3 {(0)}^{2} - 6 \cdot 0 + 9}$

Simplify $\frac{5 {(0)}^{2} - 5}{- 3 {(0)}^{2} - 6 \cdot 0 + 9}$ .

Simplify the numerator.

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

$y = \frac{5 \cdot 0 - 5}{- 3 \cdot 0^{2} - 6 \cdot 0 + 9}$

Multiply $5$ by $0$ .

$y = \frac{0 - 5}{- 3 \cdot 0^{2} - 6 \cdot 0 + 9}$

Subtract $5$ from $0$ .

$y = \frac{- 5}{- 3 \cdot 0^{2} - 6 \cdot 0 + 9}$

Simplify the denominator.

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

$y = \frac{- 5}{- 3 \cdot 0 - 6 \cdot 0 + 9}$

Multiply $- 3$ by $0$ .

$y = \frac{- 5}{0 - 6 \cdot 0 + 9}$

Multiply $- 6$ by $0$ .

$y = \frac{- 5}{0 + 0 + 9}$

Add $0$ and $0$ .

$y = \frac{- 5}{0 + 9}$

Add $0$ and $9$ .

$y = \frac{- 5}{9}$

Move the negative in front of the fraction.

$y = - \frac{5}{9}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{5}{9})$

List the intersections.

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

y-intercept(s): $(0, - \frac{5}{9})$

Find the x and y Intercepts (5x^2-5)/(-3x^2-6x+9)

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