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Pre-Algebra Examples
Step 1
Step 1.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 1.2
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 1.3
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 1.4
Since has no factors besides and .
is a prime number
Step 1.5
has factors of and .
Step 1.6
Multiply by .
Step 1.7
The factor for is itself.
occurs time.
Step 1.8
The factors for are , which is multiplied by each other times.
occurs times.
Step 1.9
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 1.10
Simplify .
Step 1.10.1
Multiply by .
Step 1.10.2
Multiply by by adding the exponents.
Step 1.10.2.1
Multiply by .
Step 1.10.2.1.1
Raise to the power of .
Step 1.10.2.1.2
Use the power rule to combine exponents.
Step 1.10.2.2
Add and .
Step 1.10.3
Multiply by by adding the exponents.
Step 1.10.3.1
Multiply by .
Step 1.10.3.1.1
Raise to the power of .
Step 1.10.3.1.2
Use the power rule to combine exponents.
Step 1.10.3.2
Add and .
Step 1.10.4
Multiply by by adding the exponents.
Step 1.10.4.1
Multiply by .
Step 1.10.4.1.1
Raise to the power of .
Step 1.10.4.1.2
Use the power rule to combine exponents.
Step 1.10.4.2
Add and .
Step 1.10.5
Multiply by by adding the exponents.
Step 1.10.5.1
Multiply by .
Step 1.10.5.1.1
Raise to the power of .
Step 1.10.5.1.2
Use the power rule to combine exponents.
Step 1.10.5.2
Add and .
Step 1.10.6
Multiply by by adding the exponents.
Step 1.10.6.1
Multiply by .
Step 1.10.6.1.1
Raise to the power of .
Step 1.10.6.1.2
Use the power rule to combine exponents.
Step 1.10.6.2
Add and .
Step 1.11
The LCM for is the numeric part multiplied by the variable part.
Step 2
Step 2.1
Multiply each term in by .
Step 2.2
Simplify the left side.
Step 2.2.1
Rewrite using the commutative property of multiplication.
Step 2.2.2
Cancel the common factor of .
Step 2.2.2.1
Factor out of .
Step 2.2.2.2
Factor out of .
Step 2.2.2.3
Cancel the common factor.
Step 2.2.2.4
Rewrite the expression.
Step 2.2.3
Combine and .
Step 2.2.4
Multiply by .
Step 2.2.5
Cancel the common factor of .
Step 2.2.5.1
Factor out of .
Step 2.2.5.2
Cancel the common factor.
Step 2.2.5.3
Rewrite the expression.
Step 2.3
Simplify the right side.
Step 2.3.1
Rewrite using the commutative property of multiplication.
Step 2.3.2
Cancel the common factor of .
Step 2.3.2.1
Factor out of .
Step 2.3.2.2
Cancel the common factor.
Step 2.3.2.3
Rewrite the expression.
Step 2.3.3
Cancel the common factor of .
Step 2.3.3.1
Cancel the common factor.
Step 2.3.3.2
Rewrite the expression.
Step 3
Step 3.1
Divide each term in by and simplify.
Step 3.1.1
Divide each term in by .
Step 3.1.2
Simplify the left side.
Step 3.1.2.1
Cancel the common factor of .
Step 3.1.2.1.1
Cancel the common factor.
Step 3.1.2.1.2
Divide by .
Step 3.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.3
Rewrite as .
Step 3.4
The complete solution is the result of both the positive and negative portions of the solution.
Step 3.4.1
First, use the positive value of the to find the first solution.
Step 3.4.2
Next, use the negative value of the to find the second solution.
Step 3.4.3
The complete solution is the result of both the positive and negative portions of the solution.