Precalculus Examples

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

Step 1

Find the x-intercepts.

Tap for more steps...

Step 1.1

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

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

Step 1.2

Set the numerator equal to zero.

$x = 0$

Step 1.3

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

Tap for more steps...

Step 2.1

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

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

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Remove parentheses.

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

Step 2.2.2

Remove parentheses.

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

Step 2.2.3

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

Tap for more steps...

Step 2.2.3.1

Cancel the common factor of $0$ and $(0) - 3$ .

Tap for more steps...

Step 2.2.3.1.1

Factor $3$ out of $0$ .

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

Step 2.2.3.1.2

Cancel the common factors.

Tap for more steps...

Step 2.2.3.1.2.1

Factor $3$ out of $0$ .

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

Step 2.2.3.1.2.2

Factor $3$ out of $- 3$ .

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

Step 2.2.3.1.2.3

Factor $3$ out of $3 \cdot 0 + 3 \cdot - 1$ .

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

Step 2.2.3.1.2.4

Cancel the common factor.

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

Step 2.2.3.1.2.5

Rewrite the expression.

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

Step 2.2.3.2

Simplify the expression.

Tap for more steps...

Step 2.2.3.2.1

Subtract $1$ from $0$ .

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

Step 2.2.3.2.2

Divide $0$ by $- 1$ .

$y = 0$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4