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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 four steps to find the LCM. Find LCM for the numeric, variable, and compound variable parts. Then, multiply them all together.
Steps to find the LCM for are:
1. Find the LCM for the numeric part .
2. Find the LCM for the variable part .
3. Find the LCM for the compound variable part .
4. Multiply each LCM together.
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
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 1.5
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 1.6
The factor for is itself.
occurs time.
Step 1.7
The factor for is itself.
occurs time.
Step 1.8
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 1.9
Multiply by .
Step 1.10
The factor for is itself.
occurs time.
Step 1.11
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Step 1.12
The Least Common Multiple of some numbers is the smallest number that the numbers are factors of.
Step 2
Step 2.1
Multiply each term in by .
Step 2.2
Simplify the left side.
Step 2.2.1
Simplify each term.
Step 2.2.1.1
Cancel the common factor of .
Step 2.2.1.1.1
Factor out of .
Step 2.2.1.1.2
Cancel the common factor.
Step 2.2.1.1.3
Rewrite the expression.
Step 2.2.1.2
Apply the distributive property.
Step 2.2.1.3
Move to the left of .
Step 2.2.1.4
Apply the distributive property.
Step 2.2.1.5
Multiply by .
Step 2.2.1.6
Cancel the common factor of .
Step 2.2.1.6.1
Move the leading negative in into the numerator.
Step 2.2.1.6.2
Factor out of .
Step 2.2.1.6.3
Cancel the common factor.
Step 2.2.1.6.4
Rewrite the expression.
Step 2.2.2
Combine the opposite terms in .
Step 2.2.2.1
Reorder the factors in the terms and .
Step 2.2.2.2
Subtract from .
Step 2.2.2.3
Add and .
Step 2.3
Simplify the right side.
Step 2.3.1
Cancel the common factor of .
Step 2.3.1.1
Factor out of .
Step 2.3.1.2
Cancel the common factor.
Step 2.3.1.3
Rewrite the expression.
Step 2.3.2
Apply the distributive property.
Step 2.3.3
Simplify the expression.
Step 2.3.3.1
Multiply by .
Step 2.3.3.2
Move to the left of .
Step 2.3.4
Apply the distributive property.
Step 2.3.5
Multiply by .
Step 3
Step 3.1
Rewrite the equation as .
Step 3.2
Add to both sides of the equation.
Step 3.3
Use the quadratic formula to find the solutions.
Step 3.4
Substitute the values , , and into the quadratic formula and solve for .
Step 3.5
Simplify.
Step 3.5.1
Simplify the numerator.
Step 3.5.1.1
Raise to the power of .
Step 3.5.1.2
Multiply .
Step 3.5.1.2.1
Multiply by .
Step 3.5.1.2.2
Multiply by .
Step 3.5.1.3
Factor out of .
Step 3.5.1.3.1
Factor out of .
Step 3.5.1.3.2
Factor out of .
Step 3.5.1.3.3
Factor out of .
Step 3.5.1.4
Rewrite as .
Step 3.5.1.4.1
Factor out of .
Step 3.5.1.4.2
Rewrite as .
Step 3.5.1.4.3
Add parentheses.
Step 3.5.1.5
Pull terms out from under the radical.
Step 3.5.2
Multiply by .
Step 3.5.3
Simplify .
Step 3.6
The final answer is the combination of both solutions.