Find the x and y Intercepts (2x-4)/(x^2-4)

$\frac{2 x - 4}{x^{2} - 4}$

Step 1

Write $\frac{2 x - 4}{x^{2} - 4}$ as an equation.

$y = \frac{2 x - 4}{x^{2} - 4}$

Step 2

Find the x-intercepts.

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

$0 = \frac{2 x - 4}{x^{2} - 4}$

Solve the equation.

Set the numerator equal to zero.

$2 x - 4 = 0$

Solve the equation for $x$ .

Add $4$ to both sides of the equation.

$2 x = 4$

Divide each term in $2 x = 4$ by $2$ and simplify.

Divide each term in $2 x = 4$ by $2$ .

$\frac{2 x}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{4}{2}$

Divide $x$ by $1$ .

$x = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$x = 2$

Exclude the solutions that do not make $0 = \frac{2 x - 4}{x^{2} - 4}$ true.

$No solution$

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

x-intercept(s): $None$

Step 3

Find the y-intercepts.

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

$y = \frac{2 (0) - 4}{{(0)}^{2} - 4}$

Solve the equation.

Remove parentheses.

$y = \frac{2 (0) - 4}{0^{2} - 4}$

Remove parentheses.

$y = \frac{2 (0) - 4}{{(0)}^{2} - 4}$

Simplify $\frac{2 (0) - 4}{{(0)}^{2} - 4}$ .

Simplify the numerator.

Multiply $2$ by $0$ .

$y = \frac{0 - 4}{0^{2} - 4}$

Subtract $4$ from $0$ .

$y = \frac{- 4}{0^{2} - 4}$

Simplify the denominator.

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

$y = \frac{- 4}{0 - 4}$

Subtract $4$ from $0$ .

$y = \frac{- 4}{- 4}$

Divide $- 4$ by $- 4$ .

$y = 1$

y-intercept(s) in point form.

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

Step 4

List the intersections.

x-intercept(s): $None$

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

Step 5

Find the x and y Intercepts (2x-4)/(x^2-4)

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