Basic Math Examples

Solve for a (1/a)b=1/(ab)
Step 1
Combine and .
Step 2
Find the LCD of the terms in the equation.
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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
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 2.5
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 2.6
The factor for is itself.
occurs time.
Step 2.7
The factor for is itself.
occurs time.
Step 2.8
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 2.9
Multiply by .
Step 3
Multiply each term in by to eliminate the fractions.
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Step 3.1
Multiply each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Cancel the common factor of .
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Step 3.2.1.1
Factor out of .
Step 3.2.1.2
Cancel the common factor.
Step 3.2.1.3
Rewrite the expression.
Step 3.2.2
Raise to the power of .
Step 3.2.3
Raise to the power of .
Step 3.2.4
Use the power rule to combine exponents.
Step 3.2.5
Add and .
Step 3.3
Simplify the right side.
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Step 3.3.1
Cancel the common factor of .
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Step 3.3.1.1
Cancel the common factor.
Step 3.3.1.2
Rewrite the expression.
Step 4
Solve the equation.
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Step 4.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 4.2
Any root of is .
Step 4.3
The complete solution is the result of both the positive and negative portions of the solution.
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Step 4.3.1
First, use the positive value of the to find the first solution.
Step 4.3.2
Next, use the negative value of the to find the second solution.
Step 4.3.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 5
The variable got canceled.
All real numbers
Step 6
The result can be shown in multiple forms.
All real numbers
Interval Notation: