Finite Math Examples

Solve for x (4x+20)/((x-3)^2)=1
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 of one and any expression is the expression.
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
Cancel the common factor of .
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Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Rewrite the expression.
Step 3.2.2
Apply the distributive property.
Step 3.2.3
Multiply by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Multiply by .
Step 4
Solve the equation.
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Step 4.1
Simplify .
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Step 4.1.1
Rewrite.
Step 4.1.2
Rewrite as .
Step 4.1.3
Expand using the FOIL Method.
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Step 4.1.3.1
Apply the distributive property.
Step 4.1.3.2
Apply the distributive property.
Step 4.1.3.3
Apply the distributive property.
Step 4.1.4
Simplify and combine like terms.
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Step 4.1.4.1
Simplify each term.
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Step 4.1.4.1.1
Multiply by .
Step 4.1.4.1.2
Move to the left of .
Step 4.1.4.1.3
Multiply by .
Step 4.1.4.2
Subtract from .
Step 4.2
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 4.3
Move all terms containing to the left side of the equation.
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Step 4.3.1
Subtract from both sides of the equation.
Step 4.3.2
Subtract from .
Step 4.4
Subtract from both sides of the equation.
Step 4.5
Subtract from .
Step 4.6
Factor using the AC method.
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Step 4.6.1
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 4.6.2
Write the factored form using these integers.
Step 4.7
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.8
Set equal to and solve for .
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Step 4.8.1
Set equal to .
Step 4.8.2
Add to both sides of the equation.
Step 4.9
Set equal to and solve for .
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Step 4.9.1
Set equal to .
Step 4.9.2
Subtract from both sides of the equation.
Step 4.10
The final solution is all the values that make true.