Algebra Examples Algebra Concepts and Expressions

Find the Holes in the Graph

$\frac{(x + 1) (x - 6)}{(x - 6) (x + 3)}$

Step 1

Cancel the common factor of $x - 6$ .

Tap for more steps...

Step 1.1

Cancel the common factor.

$\frac{(x + 1) (x - 6)}{(x - 6) (x + 3)}$

Step 1.2

Rewrite the expression.

$\frac{x + 1}{x + 3}$

Step 2

To find the holes in the graph, look at the denominator factors that were cancelled.

$x - 6$

Step 3

To find the coordinates of the holes, set each factor that was cancelled equal to $0$ , solve, and substitute back in to $\frac{x + 1}{x + 3}$ .

Tap for more steps...

Step 3.1

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Step 3.2

Add $6$ to both sides of the equation.

$x = 6$

Step 3.3

Substitute $6$ for $x$ in $\frac{x + 1}{x + 3}$ and simplify.

Tap for more steps...

Step 3.3.1

Substitute $6$ for $x$ to find the $y$ coordinate of the hole.

$\frac{6 + 1}{6 + 3}$

Step 3.3.2

Simplify.

Tap for more steps...

Step 3.3.2.1

Add $6$ and $1$ .

$\frac{7}{6 + 3}$

Step 3.3.2.2

Add $6$ and $3$ .

$\frac{7}{9}$

Step 3.4

The holes in the graph are the points where any of the cancelled factors are equal to $0$ .

$(6, \frac{7}{9})$

Step 4

Enter YOUR Problem

Algebra Concepts and Expressions

More step-by-step Algebra examples from this chapter.

How to Use Step-by-Step Examples

Read the worked problem

Each example starts from a real Algebra problem and shows the rule or formula it relies on.

Follow every step

Work through the solution line by line. Underlined terms open a glossary definition.

Solve your own problem

Enter a similar problem in the Algebra solver to get the answer with steps.

Why use Mathway?

Step-by-step solutions

See how every answer is worked out, not just the result.

Every major math subject

From basic math through calculus, statistics and chemistry.

Accurate results

Answers you can check your homework against.

Trusted by students

A reliable tool for homework and learning.

Find the Holes in the Graph

Algebra Concepts and Expressions

How to Use Step-by-Step Examples

Why use Mathway?

Explore More Algebra Help