Find the x and y Intercepts R(x)=(x^2)/(x^2+x-6)

$R (x) = \frac{x^{2}}{x^{2} + x - 6}$

Step 1

Find the x-intercepts.

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

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

Solve the equation.

Set the numerator equal to zero.

$x^{2} = 0$

Solve the equation for $x$ .

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

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = \frac{{(0)}^{2}}{{(0)}^{2} + 0 - 6}$

Solve the equation.

Remove parentheses.

$y = \frac{{(0)}^{2}}{{(0)}^{2} + 0 - 6}$

Remove parentheses.

$y = \frac{0^{2}}{{(0)}^{2} + 0 - 6}$

Remove parentheses.

$y = \frac{0^{2}}{0^{2} + 0 - 6}$

Remove parentheses.

$y = \frac{{(0)}^{2}}{{(0)}^{2} + 0 - 6}$

Simplify $\frac{{(0)}^{2}}{{(0)}^{2} + 0 - 6}$ .

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

$y = \frac{0}{0^{2} + 0 - 6}$

Simplify the denominator.

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

$y = \frac{0}{0 + 0 - 6}$

Add $0$ and $0$ .

$y = \frac{0}{0 - 6}$

Subtract $6$ from $0$ .

$y = \frac{0}{- 6}$

Divide $0$ by $- 6$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

Find the x and y Intercepts R(x)=(x^2)/(x^2+x-6)

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