Precalculus Examples

$\frac{3 x - 8}{2 x + 1}$

Step 1

Write $\frac{3 x - 8}{2 x + 1}$ as an equation.

$y = \frac{3 x - 8}{2 x + 1}$

Step 2

Find the x-intercepts.

Tap for more steps...

Step 2.1

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

$0 = \frac{3 x - 8}{2 x + 1}$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Set the numerator equal to zero.

$3 x - 8 = 0$

Step 2.2.2

Solve the equation for $x$ .

Tap for more steps...

Step 2.2.2.1

Add $8$ to both sides of the equation.

$3 x = 8$

Step 2.2.2.2

Divide each term in $3 x = 8$ by $3$ and simplify.

Tap for more steps...

Step 2.2.2.2.1

Divide each term in $3 x = 8$ by $3$ .

$\frac{3 x}{3} = \frac{8}{3}$

Step 2.2.2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{8}{3}$

Step 2.2.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{3}$

Step 2.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{8}{3}, 0)$

Step 3

Find the y-intercepts.

Tap for more steps...

Step 3.1

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

$y = \frac{3 (0) - 8}{2 (0) + 1}$

Step 3.2

Solve the equation.

Tap for more steps...

Step 3.2.1

Remove parentheses.

$y = \frac{3 (0) - 8}{2 (0) + 1}$

Step 3.2.2

Simplify $\frac{3 (0) - 8}{2 (0) + 1}$ .

Tap for more steps...

Step 3.2.2.1

Simplify the numerator.

Tap for more steps...

Step 3.2.2.1.1

Multiply $3$ by $0$ .

$y = \frac{0 - 8}{2 (0) + 1}$

Step 3.2.2.1.2

Subtract $8$ from $0$ .

$y = \frac{- 8}{2 (0) + 1}$

Step 3.2.2.2

Simplify the denominator.

Tap for more steps...

Step 3.2.2.2.1

Multiply $2$ by $0$ .

$y = \frac{- 8}{0 + 1}$

Step 3.2.2.2.2

Add $0$ and $1$ .

$y = \frac{- 8}{1}$

Step 3.2.2.3

Divide $- 8$ by $1$ .

$y = - 8$

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 8)$

Step 4

List the intersections.

x-intercept(s): $(\frac{8}{3}, 0)$

y-intercept(s): $(0, - 8)$

Step 5