Finite Math Examples

Simplify ((x-4)/(x^2-x))/((x-1)/(2x^2+3x+1)-1/(x^2-1))
Step 1
Multiply the numerator by the reciprocal of the denominator.
Step 2
Factor out of .
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Step 2.1
Factor out of .
Step 2.2
Factor out of .
Step 2.3
Factor out of .
Step 3
Factor by grouping.
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Step 3.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Step 3.1.1
Factor out of .
Step 3.1.2
Rewrite as plus
Step 3.1.3
Apply the distributive property.
Step 3.1.4
Multiply by .
Step 3.2
Factor out the greatest common factor from each group.
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Step 3.2.1
Group the first two terms and the last two terms.
Step 3.2.2
Factor out the greatest common factor (GCF) from each group.
Step 3.3
Factor the polynomial by factoring out the greatest common factor, .
Step 4
Simplify the denominator.
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Step 4.1
Rewrite as .
Step 4.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 5
Simplify the denominator.
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Step 5.1
To write as a fraction with a common denominator, multiply by .
Step 5.2
To write as a fraction with a common denominator, multiply by .
Step 5.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 5.3.1
Multiply by .
Step 5.3.2
Multiply by .
Step 5.3.3
Reorder the factors of .
Step 5.4
Combine the numerators over the common denominator.
Step 5.5
Rewrite in a factored form.
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Step 5.5.1
Expand using the FOIL Method.
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Step 5.5.1.1
Apply the distributive property.
Step 5.5.1.2
Apply the distributive property.
Step 5.5.1.3
Apply the distributive property.
Step 5.5.2
Simplify and combine like terms.
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Step 5.5.2.1
Simplify each term.
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Step 5.5.2.1.1
Multiply by .
Step 5.5.2.1.2
Move to the left of .
Step 5.5.2.1.3
Rewrite as .
Step 5.5.2.1.4
Rewrite as .
Step 5.5.2.1.5
Multiply by .
Step 5.5.2.2
Subtract from .
Step 5.5.3
Apply the distributive property.
Step 5.5.4
Multiply by .
Step 5.5.5
Multiply by .
Step 5.5.6
Subtract from .
Step 5.5.7
Subtract from .
Step 5.5.8
Add and .
Step 5.5.9
Factor out of .
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Step 5.5.9.1
Factor out of .
Step 5.5.9.2
Factor out of .
Step 5.5.9.3
Factor out of .
Step 6
Multiply the numerator by the reciprocal of the denominator.
Step 7
Multiply by .
Step 8
Cancel the common factor of .
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Step 8.1
Factor out of .
Step 8.2
Cancel the common factor.
Step 8.3
Rewrite the expression.
Step 9
Cancel the common factor of .
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Step 9.1
Factor out of .
Step 9.2
Factor out of .
Step 9.3
Cancel the common factor.
Step 9.4
Rewrite the expression.
Step 10
Multiply by .
Step 11
Raise to the power of .
Step 12
Raise to the power of .
Step 13
Use the power rule to combine exponents.
Step 14
Add and .