Finite Math Examples

Solve for y (y-c)/(y+c)+(y+c)/(y-c)=34/15
Step 1
Find the LCD of the terms in the equation.
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Step 1.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 1.2
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 1.3
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 1.4
has factors of and .
Step 1.5
Multiply by .
Step 1.6
The factor for is itself.
occurs time.
Step 1.7
The factor for is itself.
occurs time.
Step 1.8
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Step 1.9
The Least Common Multiple of some numbers is the smallest number that the numbers are factors of.
Step 2
Multiply each term in by to eliminate the fractions.
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Step 2.1
Multiply each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Simplify each term.
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Step 2.2.1.1
Rewrite using the commutative property of multiplication.
Step 2.2.1.2
Combine and .
Step 2.2.1.3
Cancel the common factor of .
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Step 2.2.1.3.1
Cancel the common factor.
Step 2.2.1.3.2
Rewrite the expression.
Step 2.2.1.4
Raise to the power of .
Step 2.2.1.5
Raise to the power of .
Step 2.2.1.6
Use the power rule to combine exponents.
Step 2.2.1.7
Add and .
Step 2.2.1.8
Rewrite using the commutative property of multiplication.
Step 2.2.1.9
Combine and .
Step 2.2.1.10
Cancel the common factor of .
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Step 2.2.1.10.1
Factor out of .
Step 2.2.1.10.2
Cancel the common factor.
Step 2.2.1.10.3
Rewrite the expression.
Step 2.2.1.11
Raise to the power of .
Step 2.2.1.12
Raise to the power of .
Step 2.2.1.13
Use the power rule to combine exponents.
Step 2.2.1.14
Add and .
Step 2.3
Simplify the right side.
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Step 2.3.1
Cancel the common factor of .
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Step 2.3.1.1
Factor out of .
Step 2.3.1.2
Cancel the common factor.
Step 2.3.1.3
Rewrite the expression.
Step 2.3.2
Expand using the FOIL Method.
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Step 2.3.2.1
Apply the distributive property.
Step 2.3.2.2
Apply the distributive property.
Step 2.3.2.3
Apply the distributive property.
Step 2.3.3
Simplify terms.
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Step 2.3.3.1
Combine the opposite terms in .
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Step 2.3.3.1.1
Reorder the factors in the terms and .
Step 2.3.3.1.2
Add and .
Step 2.3.3.1.3
Add and .
Step 2.3.3.2
Simplify each term.
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Step 2.3.3.2.1
Multiply by .
Step 2.3.3.2.2
Rewrite using the commutative property of multiplication.
Step 2.3.3.2.3
Multiply by by adding the exponents.
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Step 2.3.3.2.3.1
Move .
Step 2.3.3.2.3.2
Multiply by .
Step 2.3.3.3
Simplify by multiplying through.
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Step 2.3.3.3.1
Apply the distributive property.
Step 2.3.3.3.2
Multiply by .
Step 3
Solve the equation.
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Step 3.1
Move all terms containing to the left side of the equation.
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Step 3.1.1
Subtract from both sides of the equation.
Step 3.1.2
Simplify each term.
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Step 3.1.2.1
Rewrite as .
Step 3.1.2.2
Expand using the FOIL Method.
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Step 3.1.2.2.1
Apply the distributive property.
Step 3.1.2.2.2
Apply the distributive property.
Step 3.1.2.2.3
Apply the distributive property.
Step 3.1.2.3
Simplify and combine like terms.
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Step 3.1.2.3.1
Simplify each term.
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Step 3.1.2.3.1.1
Multiply by .
Step 3.1.2.3.1.2
Rewrite using the commutative property of multiplication.
Step 3.1.2.3.1.3
Rewrite using the commutative property of multiplication.
Step 3.1.2.3.1.4
Multiply by by adding the exponents.
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Step 3.1.2.3.1.4.1
Move .
Step 3.1.2.3.1.4.2
Multiply by .
Step 3.1.2.3.1.5
Multiply by .
Step 3.1.2.3.1.6
Multiply by .
Step 3.1.2.3.2
Subtract from .
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Step 3.1.2.3.2.1
Move .
Step 3.1.2.3.2.2
Subtract from .
Step 3.1.2.4
Apply the distributive property.
Step 3.1.2.5
Multiply by .
Step 3.1.2.6
Rewrite as .
Step 3.1.2.7
Expand using the FOIL Method.
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Step 3.1.2.7.1
Apply the distributive property.
Step 3.1.2.7.2
Apply the distributive property.
Step 3.1.2.7.3
Apply the distributive property.
Step 3.1.2.8
Simplify and combine like terms.
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Step 3.1.2.8.1
Simplify each term.
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Step 3.1.2.8.1.1
Multiply by .
Step 3.1.2.8.1.2
Multiply by .
Step 3.1.2.8.2
Add and .
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Step 3.1.2.8.2.1
Reorder and .
Step 3.1.2.8.2.2
Add and .
Step 3.1.2.9
Apply the distributive property.
Step 3.1.2.10
Multiply by .
Step 3.1.3
Combine the opposite terms in .
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Step 3.1.3.1
Add and .
Step 3.1.3.2
Add and .
Step 3.1.4
Add and .
Step 3.1.5
Add and .
Step 3.1.6
Subtract from .
Step 3.2
Move all terms not containing to the right side of the equation.
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Step 3.2.1
Subtract from both sides of the equation.
Step 3.2.2
Subtract from .
Step 3.3
Divide each term in by and simplify.
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Step 3.3.1
Divide each term in by .
Step 3.3.2
Simplify the left side.
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Step 3.3.2.1
Cancel the common factor of .
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Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Divide by .
Step 3.3.3
Simplify the right side.
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Step 3.3.3.1
Cancel the common factor of and .
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Step 3.3.3.1.1
Factor out of .
Step 3.3.3.1.2
Cancel the common factors.
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Step 3.3.3.1.2.1
Factor out of .
Step 3.3.3.1.2.2
Cancel the common factor.
Step 3.3.3.1.2.3
Rewrite the expression.
Step 3.3.3.1.2.4
Divide by .
Step 3.4
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.5
Simplify .
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Step 3.5.1
Rewrite as .
Step 3.5.2
Pull terms out from under the radical, assuming positive real numbers.
Step 3.6
The complete solution is the result of both the positive and negative portions of the solution.
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Step 3.6.1
First, use the positive value of the to find the first solution.
Step 3.6.2
Next, use the negative value of the to find the second solution.
Step 3.6.3
The complete solution is the result of both the positive and negative portions of the solution.