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

$\frac{3 x - 3}{x^{2} - 1}$

Write $\frac{3 x - 3}{x^{2} - 1}$ as an equation.

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

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 $x$ .

Add $3$ to 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): $None$

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

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

Simplify the numerator.

Multiply $3$ by $0$ .

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

Subtract $3$ from $0$ .

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

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): $(0, 3)$

List the intersections.

x-intercept(s): $None$

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

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

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