# Precalculus Examples

Step 1

Step 1.1

Subtract from 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

Subtract from .

Step 2

Step 2.1

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

Step 2.2

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 2.3

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 2.4

Since has no factors besides and .

is a prime number

Step 2.5

Since has no factors besides and .

is a prime number

Step 2.6

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

Step 2.7

Multiply by .

Step 2.8

The factor for is itself.

occurs time.

Step 2.9

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

Step 2.10

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

Step 3

Step 3.1

Multiply each term in by .

Step 3.2

Simplify the left side.

Step 3.2.1

Rewrite using the commutative property of multiplication.

Step 3.2.2

Cancel the common factor of .

Step 3.2.2.1

Factor out of .

Step 3.2.2.2

Factor out of .

Step 3.2.2.3

Cancel the common factor.

Step 3.2.2.4

Rewrite the expression.

Step 3.2.3

Combine and .

Step 3.2.4

Multiply by .

Step 3.2.5

Cancel the common factor of .

Step 3.2.5.1

Cancel the common factor.

Step 3.2.5.2

Rewrite the expression.

Step 3.3

Simplify the right side.

Step 3.3.1

Cancel the common factor of .

Step 3.3.1.1

Factor out of .

Step 3.3.1.2

Cancel the common factor.

Step 3.3.1.3

Rewrite the expression.

Step 3.3.2

Multiply by .

Step 4

Step 4.1

Rewrite the equation as .

Step 4.2

Divide each term in by and simplify.

Step 4.2.1

Divide each term in by .

Step 4.2.2

Simplify the left side.

Step 4.2.2.1

Cancel the common factor of .

Step 4.2.2.1.1

Cancel the common factor.

Step 4.2.2.1.2

Divide by .

Step 4.2.3

Simplify the right side.

Step 4.2.3.1

Cancel the common factor of and .

Step 4.2.3.1.1

Factor out of .

Step 4.2.3.1.2

Cancel the common factors.

Step 4.2.3.1.2.1

Factor out of .

Step 4.2.3.1.2.2

Cancel the common factor.

Step 4.2.3.1.2.3

Rewrite the expression.

Step 5

The result can be shown in multiple forms.

Exact Form:

Decimal Form: