Basic Math Examples

Solve for z (2z)/2+2/z=6/(2z)
Step 1
Factor each term.
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Step 1.1
Reduce the expression by cancelling the common factors.
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Step 1.1.1
Reduce the expression by cancelling the common factors.
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Step 1.1.1.1
Cancel the common factor.
Step 1.1.1.2
Rewrite the expression.
Step 1.1.2
Divide by .
Step 1.2
Reduce the expression by cancelling the common factors.
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Step 1.2.1
Factor out of .
Step 1.2.2
Factor out of .
Step 1.2.3
Cancel the common factor.
Step 1.2.4
Rewrite the expression.
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 LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
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
Simplify each term.
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Step 3.2.1.1
Multiply by .
Step 3.2.1.2
Cancel the common factor of .
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Step 3.2.1.2.1
Cancel the common factor.
Step 3.2.1.2.2
Rewrite the expression.
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
Move all terms not containing to the right side of the equation.
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Step 4.1.1
Subtract from both sides of the equation.
Step 4.1.2
Subtract from .
Step 4.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 4.3
Any root of is .
Step 4.4
The complete solution is the result of both the positive and negative portions of the solution.
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Step 4.4.1
First, use the positive value of the to find the first solution.
Step 4.4.2
Next, use the negative value of the to find the second solution.
Step 4.4.3
The complete solution is the result of both the positive and negative portions of the solution.