Finite Math Examples

Solve for a 2/3+(3-7a)/(21a-63)=(7a+1)/(a-3)
Step 1
Factor out of .
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Step 1.1
Factor out of .
Step 1.2
Factor out of .
Step 1.3
Factor out of .
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
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 2.3
Since has no factors besides and .
is a prime number
Step 2.4
has factors of and .
Step 2.5
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 2.6
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 2.7
Multiply by .
Step 2.8
The factor for is itself.
occurs time.
Step 2.9
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Step 2.10
The Least Common Multiple of some numbers is the smallest number that the numbers are factors of.
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
Cancel the common factor of .
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Step 3.2.1.1.1
Factor out of .
Step 3.2.1.1.2
Cancel the common factor.
Step 3.2.1.1.3
Rewrite the expression.
Step 3.2.1.2
Multiply by .
Step 3.2.1.3
Apply the distributive property.
Step 3.2.1.4
Multiply by .
Step 3.2.1.5
Rewrite using the commutative property of multiplication.
Step 3.2.1.6
Cancel the common factor of .
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Step 3.2.1.6.1
Cancel the common factor.
Step 3.2.1.6.2
Rewrite the expression.
Step 3.2.1.7
Cancel the common factor of .
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Step 3.2.1.7.1
Cancel the common factor.
Step 3.2.1.7.2
Rewrite the expression.
Step 3.2.2
Simplify by adding terms.
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Step 3.2.2.1
Subtract from .
Step 3.2.2.2
Add and .
Step 3.3
Simplify the right side.
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Step 3.3.1
Rewrite using the commutative property of multiplication.
Step 3.3.2
Combine and .
Step 3.3.3
Cancel the common factor of .
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Step 3.3.3.1
Cancel the common factor.
Step 3.3.3.2
Rewrite the expression.
Step 3.3.4
Apply the distributive property.
Step 3.3.5
Multiply.
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Step 3.3.5.1
Multiply by .
Step 3.3.5.2
Multiply by .
Step 4
Solve the equation.
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Step 4.1
Move all terms containing to the left 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
Move all terms not containing to the right side of the equation.
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Step 4.2.1
Add to both sides of the equation.
Step 4.2.2
Add and .
Step 4.3
Divide each term in by and simplify.
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Step 4.3.1
Divide each term in by .
Step 4.3.2
Simplify the left side.
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Step 4.3.2.1
Cancel the common factor of .
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Step 4.3.2.1.1
Cancel the common factor.
Step 4.3.2.1.2
Divide by .
Step 4.3.3
Simplify the right side.
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Step 4.3.3.1
Cancel the common factor of and .
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Step 4.3.3.1.1
Factor out of .
Step 4.3.3.1.2
Cancel the common factors.
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Step 4.3.3.1.2.1
Factor out of .
Step 4.3.3.1.2.2
Cancel the common factor.
Step 4.3.3.1.2.3
Rewrite the expression.
Step 4.3.3.2
Move the negative in front of the fraction.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: