Basic Math Examples

Solve for a 1/3*(4a+1)=1/(2a)
Step 1
Simplify .
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Step 1.1
Apply the distributive property.
Step 1.2
Multiply .
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Step 1.2.1
Combine and .
Step 1.2.2
Combine and .
Step 1.3
Multiply by .
Step 2
Subtract from both sides of the equation.
Step 3
Find the LCD of the terms in the equation.
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Step 3.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 3.2
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 3.3
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 3.4
Since has no factors besides and .
is a prime number
Step 3.5
Since has no factors besides and .
is a prime number
Step 3.6
Since has no factors besides and .
is a prime number
Step 3.7
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 3.8
Multiply by .
Step 3.9
The factor for is itself.
occurs time.
Step 3.10
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 3.11
The LCM for is the numeric part multiplied by the variable part.
Step 4
Multiply each term in by to eliminate the fractions.
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Step 4.1
Multiply each term in by .
Step 4.2
Simplify the left side.
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Step 4.2.1
Rewrite using the commutative property of multiplication.
Step 4.2.2
Cancel the common factor of .
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Step 4.2.2.1
Factor out of .
Step 4.2.2.2
Cancel the common factor.
Step 4.2.2.3
Rewrite the expression.
Step 4.2.3
Multiply by .
Step 4.2.4
Multiply by by adding the exponents.
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Step 4.2.4.1
Move .
Step 4.2.4.2
Multiply by .
Step 4.3
Simplify the right side.
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Step 4.3.1
Simplify each term.
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Step 4.3.1.1
Rewrite using the commutative property of multiplication.
Step 4.3.1.2
Cancel the common factor of .
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Step 4.3.1.2.1
Factor out of .
Step 4.3.1.2.2
Factor out of .
Step 4.3.1.2.3
Cancel the common factor.
Step 4.3.1.2.4
Rewrite the expression.
Step 4.3.1.3
Combine and .
Step 4.3.1.4
Cancel the common factor of .
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Step 4.3.1.4.1
Cancel the common factor.
Step 4.3.1.4.2
Rewrite the expression.
Step 4.3.1.5
Cancel the common factor of .
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Step 4.3.1.5.1
Move the leading negative in into the numerator.
Step 4.3.1.5.2
Factor out of .
Step 4.3.1.5.3
Cancel the common factor.
Step 4.3.1.5.4
Rewrite the expression.
Step 4.3.1.6
Multiply by .
Step 5
Solve the equation.
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Step 5.1
Add to both sides of the equation.
Step 5.2
Subtract from both sides of the equation.
Step 5.3
Factor by grouping.
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Step 5.3.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Step 5.3.1.1
Factor out of .
Step 5.3.1.2
Rewrite as plus
Step 5.3.1.3
Apply the distributive property.
Step 5.3.2
Factor out the greatest common factor from each group.
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Step 5.3.2.1
Group the first two terms and the last two terms.
Step 5.3.2.2
Factor out the greatest common factor (GCF) from each group.
Step 5.3.3
Factor the polynomial by factoring out the greatest common factor, .
Step 5.4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 5.5
Set equal to and solve for .
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Step 5.5.1
Set equal to .
Step 5.5.2
Solve for .
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Step 5.5.2.1
Add to both sides of the equation.
Step 5.5.2.2
Divide each term in by and simplify.
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Step 5.5.2.2.1
Divide each term in by .
Step 5.5.2.2.2
Simplify the left side.
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Step 5.5.2.2.2.1
Cancel the common factor of .
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Step 5.5.2.2.2.1.1
Cancel the common factor.
Step 5.5.2.2.2.1.2
Divide by .
Step 5.6
Set equal to and solve for .
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Step 5.6.1
Set equal to .
Step 5.6.2
Solve for .
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Step 5.6.2.1
Subtract from both sides of the equation.
Step 5.6.2.2
Divide each term in by and simplify.
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Step 5.6.2.2.1
Divide each term in by .
Step 5.6.2.2.2
Simplify the left side.
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Step 5.6.2.2.2.1
Cancel the common factor of .
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Step 5.6.2.2.2.1.1
Cancel the common factor.
Step 5.6.2.2.2.1.2
Divide by .
Step 5.6.2.2.3
Simplify the right side.
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Step 5.6.2.2.3.1
Move the negative in front of the fraction.
Step 5.7
The final solution is all the values that make true.
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: