Basic Math Examples

Solve for b b/2-31/6=b/3+5/b
Step 1
Add to both sides of the equation.
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
Since has no factors besides and .
is a prime number
Step 2.5
Since has no factors besides and .
is a prime number
Step 2.6
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 2.7
has factors of and .
Step 2.8
Multiply by .
Step 2.9
The factor for is itself.
occurs time.
Step 2.10
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 2.11
The LCM for is the numeric part multiplied by the variable part.
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
Rewrite using the commutative property of multiplication.
Step 3.2.2
Cancel the common factor of .
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Step 3.2.2.1
Factor out of .
Step 3.2.2.2
Cancel the common factor.
Step 3.2.2.3
Rewrite the expression.
Step 3.2.3
Multiply by by adding the exponents.
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Step 3.2.3.1
Move .
Step 3.2.3.2
Multiply by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Simplify each term.
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Step 3.3.1.1
Rewrite using the commutative property of multiplication.
Step 3.3.1.2
Cancel the common factor of .
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Step 3.3.1.2.1
Factor out of .
Step 3.3.1.2.2
Cancel the common factor.
Step 3.3.1.2.3
Rewrite the expression.
Step 3.3.1.3
Multiply by by adding the exponents.
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Step 3.3.1.3.1
Move .
Step 3.3.1.3.2
Multiply by .
Step 3.3.1.4
Rewrite using the commutative property of multiplication.
Step 3.3.1.5
Multiply .
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Step 3.3.1.5.1
Combine and .
Step 3.3.1.5.2
Multiply by .
Step 3.3.1.6
Cancel the common factor of .
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Step 3.3.1.6.1
Cancel the common factor.
Step 3.3.1.6.2
Rewrite the expression.
Step 3.3.1.7
Cancel the common factor of .
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Step 3.3.1.7.1
Factor out of .
Step 3.3.1.7.2
Cancel the common factor.
Step 3.3.1.7.3
Rewrite the expression.
Step 4
Solve the equation.
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Step 4.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 4.2
Move all terms containing to the left side of the equation.
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Step 4.2.1
Subtract from both sides of the equation.
Step 4.2.2
Subtract from .
Step 4.3
Use the quadratic formula to find the solutions.
Step 4.4
Substitute the values , , and into the quadratic formula and solve for .
Step 4.5
Simplify.
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Step 4.5.1
Simplify the numerator.
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Step 4.5.1.1
Raise to the power of .
Step 4.5.1.2
Multiply .
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Step 4.5.1.2.1
Multiply by .
Step 4.5.1.2.2
Multiply by .
Step 4.5.1.3
Add and .
Step 4.5.2
Multiply by .
Step 4.5.3
Simplify .
Step 4.6
The final answer is the combination of both solutions.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: