Finite Math Examples

Solve by Factoring 20((x-5)/11-(x-11)/5)=1
Step 1
Subtract from both sides of the equation.
Step 2
Simplify .
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Step 2.1
Simplify each term.
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Step 2.1.1
To write as a fraction with a common denominator, multiply by .
Step 2.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 2.1.3.1
Multiply by .
Step 2.1.3.2
Multiply by .
Step 2.1.3.3
Multiply by .
Step 2.1.3.4
Multiply by .
Step 2.1.4
Combine the numerators over the common denominator.
Step 2.1.5
Simplify the numerator.
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Step 2.1.5.1
Apply the distributive property.
Step 2.1.5.2
Move to the left of .
Step 2.1.5.3
Multiply by .
Step 2.1.5.4
Apply the distributive property.
Step 2.1.5.5
Multiply by .
Step 2.1.5.6
Apply the distributive property.
Step 2.1.5.7
Multiply by .
Step 2.1.5.8
Multiply by .
Step 2.1.5.9
Subtract from .
Step 2.1.5.10
Add and .
Step 2.1.5.11
Factor out of .
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Step 2.1.5.11.1
Factor out of .
Step 2.1.5.11.2
Factor out of .
Step 2.1.5.11.3
Factor out of .
Step 2.1.6
Cancel the common factor of .
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Step 2.1.6.1
Factor out of .
Step 2.1.6.2
Factor out of .
Step 2.1.6.3
Cancel the common factor.
Step 2.1.6.4
Rewrite the expression.
Step 2.1.7
Combine and .
Step 2.1.8
Multiply by .
Step 2.2
To write as a fraction with a common denominator, multiply by .
Step 2.3
Combine and .
Step 2.4
Combine the numerators over the common denominator.
Step 2.5
Simplify the numerator.
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Step 2.5.1
Apply the distributive property.
Step 2.5.2
Multiply by .
Step 2.5.3
Multiply by .
Step 2.5.4
Multiply by .
Step 2.5.5
Subtract from .
Step 2.6
Factor out of .
Step 2.7
Rewrite as .
Step 2.8
Factor out of .
Step 2.9
Rewrite as .
Step 2.10
Move the negative in front of the fraction.
Step 3
Set the numerator equal to zero.
Step 4
Solve the equation for .
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Step 4.1
Add to both sides of the equation.
Step 4.2
Divide each term in by and simplify.
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Step 4.2.1
Divide each term in by .
Step 4.2.2
Simplify the left side.
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Step 4.2.2.1
Cancel the common factor of .
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Step 4.2.2.1.1
Cancel the common factor.
Step 4.2.2.1.2
Divide by .