Find the x and y Intercepts f(x)=(-3x+3)/(x^2-1)

$f (x) = \frac{- 3 x + 3}{x^{2} - 1}$

Step 1

Find the x-intercepts.

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

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

Solve the equation.

Set the numerator equal to zero.

$- 3 x + 3 = 0$

Solve the equation for $x$ .

Subtract $3$ from both sides of the equation.

$- 3 x = - 3$

Divide each term in $- 3 x = - 3$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 3$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 3}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 3}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 3}{- 3}$

Simplify the right side.

Divide $- 3$ by $- 3$ .

$x = 1$

Exclude the solutions that do not make $0 = \frac{- 3 x + 3}{x^{2} - 1}$ true.

$No solution$

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

x-intercept(s): $None$

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

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

Simplify the numerator.

Multiply $- 3$ by $0$ .

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

Add $0$ and $3$ .

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

Simplify the denominator.

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

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

Subtract $1$ from $0$ .

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

Divide $3$ by $- 1$ .

$y = - 3$

y-intercept(s) in point form.

y-intercept(s): $(0, - 3)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - 3)$

Step 4

Find the x and y Intercepts f(x)=(-3x+3)/(x^2-1)

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