Enter a problem...
Trigonometry 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
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 1.5
The prime factors for are .
Step 1.5.1
has factors of and .
Step 1.5.2
has factors of and .
Step 1.5.3
has factors of and .
Step 1.6
Multiply .
Step 1.6.1
Multiply by .
Step 1.6.2
Multiply by .
Step 1.6.3
Multiply by .
Step 1.7
The factors for are , which is multiplied by each other times.
occurs times.
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 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
Combine and .
Step 2.2.3
Cancel the common factor of .
Step 2.2.3.1
Cancel the common factor.
Step 2.2.3.2
Rewrite the expression.
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 3
Step 3.1
Rewrite the equation as .
Step 3.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.3
Simplify .
Step 3.3.1
Rewrite as .
Step 3.3.2
Pull terms out from under the radical, assuming positive real numbers.
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.