Finite Math Examples

Solve for c x/(c-2)=cx+3
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
Remove parentheses.
Step 1.3
The LCM of one and any expression is the expression.
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
Cancel the common factor of .
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Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Rewrite the expression.
Step 2.3
Simplify the right side.
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Step 2.3.1
Simplify each term.
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Step 2.3.1.1
Apply the distributive property.
Step 2.3.1.2
Multiply by by adding the exponents.
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Step 2.3.1.2.1
Move .
Step 2.3.1.2.2
Multiply by .
Step 2.3.1.3
Move to the left of .
Step 2.3.1.4
Remove parentheses.
Step 2.3.1.5
Apply the distributive property.
Step 2.3.1.6
Multiply by .
Step 3
Solve the equation.
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Step 3.1
Rewrite the equation as .
Step 3.2
Subtract from both sides of the equation.
Step 3.3
Use the quadratic formula to find the solutions.
Step 3.4
Substitute the values , , and into the quadratic formula and solve for .
Step 3.5
Simplify the numerator.
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Step 3.5.1
Apply the distributive property.
Step 3.5.2
Multiply by .
Step 3.5.3
Multiply by .
Step 3.5.4
Rewrite as .
Step 3.5.5
Expand using the FOIL Method.
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Step 3.5.5.1
Apply the distributive property.
Step 3.5.5.2
Apply the distributive property.
Step 3.5.5.3
Apply the distributive property.
Step 3.5.6
Simplify and combine like terms.
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Step 3.5.6.1
Simplify each term.
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Step 3.5.6.1.1
Rewrite using the commutative property of multiplication.
Step 3.5.6.1.2
Multiply by by adding the exponents.
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Step 3.5.6.1.2.1
Move .
Step 3.5.6.1.2.2
Multiply by .
Step 3.5.6.1.3
Multiply by .
Step 3.5.6.1.4
Multiply by .
Step 3.5.6.1.5
Multiply by .
Step 3.5.6.1.6
Multiply by .
Step 3.5.6.2
Subtract from .
Step 3.5.7
Apply the distributive property.
Step 3.5.8
Multiply by .
Step 3.5.9
Rewrite using the commutative property of multiplication.
Step 3.5.10
Simplify each term.
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Step 3.5.10.1
Multiply by by adding the exponents.
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Step 3.5.10.1.1
Move .
Step 3.5.10.1.2
Multiply by .
Step 3.5.10.2
Multiply by .
Step 3.5.11
Add and .
Step 3.5.12
Add and .
Step 3.6
The final answer is the combination of both solutions.