Find the x and y Intercepts (3x)/(2x^2-72)

$\frac{3 x}{2 x^{2} - 72}$

Step 1

Write $\frac{3 x}{2 x^{2} - 72}$ as an equation.

$y = \frac{3 x}{2 x^{2} - 72}$

Step 2

Find the x-intercepts.

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

$0 = \frac{3 x}{2 x^{2} - 72}$

Solve the equation.

Set the numerator equal to zero.

$3 x = 0$

Divide each term in $3 x = 0$ by $3$ and simplify.

Divide each term in $3 x = 0$ by $3$ .

$\frac{3 x}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{0}{3}$

Divide $x$ by $1$ .

$x = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$x = 0$

x-intercept(s) in point form.

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

Step 3

Find the y-intercepts.

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

$y = \frac{3 (0)}{2 {(0)}^{2} - 72}$

Solve the equation.

Remove parentheses.

$y = \frac{3 (0)}{2 \cdot 0^{2} - 72}$

Remove parentheses.

$y = \frac{3 (0)}{2 {(0)}^{2} - 72}$

Simplify $\frac{3 (0)}{2 {(0)}^{2} - 72}$ .

Cancel the common factor of $0$ and $2 {(0)}^{2} - 72$ .

Factor $2$ out of $3 (0)$ .

$y = \frac{2 (3 \cdot (0))}{2 {(0)}^{2} - 72}$

Cancel the common factors.

Factor $2$ out of $2 {(0)}^{2}$ .

$y = \frac{2 (3 \cdot (0))}{2 ({(0)}^{2}) - 72}$

Factor $2$ out of $- 72$ .

$y = \frac{2 (3 \cdot (0))}{2 ({(0)}^{2}) + 2 (- 36)}$

Factor $2$ out of $2 ({(0)}^{2}) + 2 (- 36)$ .

$y = \frac{2 (3 \cdot (0))}{2 ({(0)}^{2} - 36)}$

Cancel the common factor.

$y = \frac{2 (3 \cdot (0))}{2 ({(0)}^{2} - 36)}$

Rewrite the expression.

$y = \frac{3 \cdot (0)}{{(0)}^{2} - 36}$

Multiply $3$ by $0$ .

$y = \frac{0}{0^{2} - 36}$

Simplify the denominator.

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

$y = \frac{0}{0 - 36}$

Subtract $36$ from $0$ .

$y = \frac{0}{- 36}$

Divide $0$ by $- 36$ .

$y = 0$

y-intercept(s) in point form.

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

Step 4

List the intersections.

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

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

Step 5

Find the x and y Intercepts (3x)/(2x^2-72)

Related Questions

Support LCMGCF.com by disabling your adblocker.