Finite Math Examples

Simplify 6/(50+23x^2-x^4)-3/(x^3-5x^2+2x-10)
Step 1
Simplify each term.
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Step 1.1
Simplify the denominator.
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Step 1.1.1
Factor by grouping.
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Step 1.1.1.1
Reorder terms.
Step 1.1.1.2
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 1.1.1.2.1
Factor out of .
Step 1.1.1.2.2
Rewrite as plus
Step 1.1.1.2.3
Apply the distributive property.
Step 1.1.1.3
Factor out the greatest common factor from each group.
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Step 1.1.1.3.1
Group the first two terms and the last two terms.
Step 1.1.1.3.2
Factor out the greatest common factor (GCF) from each group.
Step 1.1.1.4
Factor the polynomial by factoring out the greatest common factor, .
Step 1.1.2
Rewrite as .
Step 1.1.3
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 1.2
Simplify the denominator.
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Step 1.2.1
Factor out the greatest common factor from each group.
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Step 1.2.1.1
Group the first two terms and the last two terms.
Step 1.2.1.2
Factor out the greatest common factor (GCF) from each group.
Step 1.2.2
Factor the polynomial by factoring out the greatest common factor, .
Step 2
Simplify with factoring out.
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Step 2.1
Factor out of .
Step 2.2
Rewrite as .
Step 2.3
Factor out of .
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
To write as a fraction with a common denominator, multiply by .
Step 5
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 5.1
Multiply by .
Step 5.2
Multiply by .
Step 5.3
Reorder the factors of .
Step 5.4
Reorder the factors of .
Step 6
Combine the numerators over the common denominator.
Step 7
Simplify the numerator.
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Step 7.1
Factor out of .
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Step 7.1.1
Reorder and .
Step 7.1.2
Factor out of .
Step 7.1.3
Factor out of .
Step 7.2
Multiply by .
Step 7.3
Add and .
Step 8
Simplify terms.
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Step 8.1
Dividing two negative values results in a positive value.
Step 8.2
Factor out of .
Step 8.3
Rewrite as .
Step 8.4
Factor out of .
Step 8.5
Rewrite negatives.
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Step 8.5.1
Rewrite as .
Step 8.5.2
Move the negative in front of the fraction.