# Precalculus Examples

Step 1

Subtract from both sides of the equation.

Step 2

Move the negative in front of the fraction.

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

Since has no factors besides and .

is a prime number

Step 3.5

has factors of and .

Step 3.6

Multiply by .

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

Move the leading negative in into the numerator.

Step 4.3.1.2

Factor out of .

Step 4.3.1.3

Cancel the common factor.

Step 4.3.1.4

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

Dividing two negative values results in a positive value.

Step 5.2.2.2

Divide by .

Step 5.2.3

Simplify the right side.

Step 5.2.3.1

Divide by .