# Precalculus Examples

Step 1

Step 1.1

Add to both sides of the equation.

Step 1.2

To write as a fraction with a common denominator, multiply by .

Step 1.3

Combine and .

Step 1.4

Combine the numerators over the common denominator.

Step 1.5

Simplify the numerator.

Step 1.5.1

Multiply by .

Step 1.5.2

Add and .

Step 2

Step 2.1

Cancel the common factor.

Step 2.2

Rewrite the expression.

Step 3

Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

Step 3.2

Since contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .

Step 3.3

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

Step 3.4

The number is not a prime number because it only has one positive factor, which is itself.

Not prime

Step 3.5

Since has no factors besides and .

is a prime number

Step 3.6

The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.

Step 3.7

The factor for is itself.

occurs time.

Step 3.8

The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.

Step 3.9

The LCM for is the numeric part multiplied by the variable part.

Step 4

Step 4.1

Multiply each term in by .

Step 4.2

Simplify the left side.

Step 4.2.1

Cancel the common factor of .

Step 4.2.1.1

Move the leading negative in into the numerator.

Step 4.2.1.2

Factor out of .

Step 4.2.1.3

Cancel the common factor.

Step 4.2.1.4

Rewrite the expression.

Step 4.2.2

Multiply by .

Step 4.3

Simplify the right side.

Step 4.3.1

Cancel the common factor of .

Step 4.3.1.1

Factor out of .

Step 4.3.1.2

Cancel the common factor.

Step 4.3.1.3

Rewrite the expression.

Step 5

Step 5.1

Rewrite the equation as .

Step 5.2

Divide each term in by and simplify.

Step 5.2.1

Divide each term in by .

Step 5.2.2

Simplify the left side.

Step 5.2.2.1

Cancel the common factor of .

Step 5.2.2.1.1

Cancel the common factor.

Step 5.2.2.1.2

Divide by .

Step 5.2.3

Simplify the right side.

Step 5.2.3.1

Move the negative in front of the fraction.

Step 6

The result can be shown in multiple forms.

Exact Form:

Decimal Form: