Finite Math Examples

Solve for y 4/(y^2-7y+10)-1/(y-5)=1/(8y-16)
Step 1
Factor each term.
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Step 1.1
Factor using the AC method.
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Step 1.1.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 1.1.2
Write the factored form using these integers.
Step 1.2
Factor out of .
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Step 1.2.1
Factor out of .
Step 1.2.2
Factor out of .
Step 1.2.3
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
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 2.4
The prime factors for are .
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Step 2.4.1
has factors of and .
Step 2.4.2
has factors of and .
Step 2.5
Multiply .
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Step 2.5.1
Multiply by .
Step 2.5.2
Multiply by .
Step 2.6
The factor for is itself.
occurs time.
Step 2.7
The factor for is itself.
occurs time.
Step 2.8
The factor for is itself.
occurs time.
Step 2.9
The factor for is itself.
occurs time.
Step 2.10
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Step 2.11
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
Rewrite using the commutative property of multiplication.
Step 3.2.1.2
Multiply .
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Step 3.2.1.2.1
Combine and .
Step 3.2.1.2.2
Multiply by .
Step 3.2.1.3
Cancel the common factor of .
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Step 3.2.1.3.1
Cancel the common factor.
Step 3.2.1.3.2
Rewrite the expression.
Step 3.2.1.4
Cancel the common factor of .
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Step 3.2.1.4.1
Move the leading negative in into the numerator.
Step 3.2.1.4.2
Factor out of .
Step 3.2.1.4.3
Cancel the common factor.
Step 3.2.1.4.4
Rewrite the expression.
Step 3.2.1.5
Multiply by .
Step 3.2.1.6
Apply the distributive property.
Step 3.2.1.7
Multiply by .
Step 3.2.2
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
Cancel the common factor of .
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Step 3.3.2.1
Cancel the common factor.
Step 3.3.2.2
Rewrite the expression.
Step 3.3.3
Cancel the common factor of .
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Step 3.3.3.1
Factor out of .
Step 3.3.3.2
Cancel the common factor.
Step 3.3.3.3
Rewrite the expression.
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
Subtract from both sides of the equation.
Step 4.2.2
Subtract from .
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
Dividing two negative values results in a positive value.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: