Find the x and y Intercepts y=(81-x^2)/(7+x^2)

$y = \frac{81 - x^{2}}{7 + x^{2}}$

Step 1

Find the x-intercepts.

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

$0 = \frac{81 - x^{2}}{7 + x^{2}}$

Solve the equation.

Set the numerator equal to zero.

$81 - x^{2} = 0$

Solve the equation for $x$ .

Subtract $81$ from both sides of the equation.

$- x^{2} = - 81$

Divide each term in $- x^{2} = - 81$ by $- 1$ and simplify.

Divide each term in $- x^{2} = - 81$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{- 81}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{- 81}{- 1}$

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

$x^{2} = \frac{- 81}{- 1}$

Simplify the right side.

Divide $- 81$ by $- 1$ .

$x^{2} = 81$

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

$x = \pm \sqrt{81}$

Simplify $\pm \sqrt{81}$ .

Rewrite $81$ as $9^{2}$ .

$x = \pm \sqrt{9^{2}}$

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

$x = \pm 9$

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.

$x = 9$

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

$x = - 9$

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

$x = 9, - 9$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = \frac{81 - {(0)}^{2}}{7 + {(0)}^{2}}$

Solve the equation.

Remove parentheses.

$y = \frac{81 - 0^{2}}{7 + {(0)}^{2}}$

Remove parentheses.

$y = \frac{81 - 0^{2}}{7 + 0^{2}}$

Remove parentheses.

$y = \frac{81 - {(0)}^{2}}{7 + {(0)}^{2}}$

Simplify $\frac{81 - {(0)}^{2}}{7 + {(0)}^{2}}$ .

Simplify the numerator.

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

$y = \frac{81 - 0}{7 + 0^{2}}$

Multiply $- 1$ by $0$ .

$y = \frac{81 + 0}{7 + 0^{2}}$

Add $81$ and $0$ .

$y = \frac{81}{7 + 0^{2}}$

Simplify the denominator.

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

$y = \frac{81}{7 + 0}$

Add $7$ and $0$ .

$y = \frac{81}{7}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{81}{7})$

Step 3

List the intersections.

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

y-intercept(s): $(0, \frac{81}{7})$

Step 4

Find the x and y Intercepts y=(81-x^2)/(7+x^2)

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