Algebra Examples

Simplify (c+6b)/(ac+2bc-6ab-3a^2)+(2b)/(a^2+2ab)-b/(ac-3a^2)
Step 1
Simplify each term.
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Step 1.1
Simplify the denominator.
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Step 1.1.1
Reorder terms.
Step 1.1.2
Factor out the greatest common factor from each group.
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Step 1.1.2.1
Group the first two terms and the last two terms.
Step 1.1.2.2
Factor out the greatest common factor (GCF) from each group.
Step 1.1.3
Factor the polynomial by factoring out the greatest common factor, .
Step 1.2
Factor out of .
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Step 1.2.1
Factor out of .
Step 1.2.2
Factor out of .
Step 1.2.3
Factor out of .
Step 1.3
Factor out of .
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Step 1.3.1
Factor out of .
Step 1.3.2
Factor out of .
Step 1.3.3
Factor out of .
Step 2
To write as a fraction with a common denominator, multiply by .
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 4.1
Multiply by .
Step 4.2
Multiply by .
Step 4.3
Reorder the factors of .
Step 4.4
Reorder the factors of .
Step 5
Combine the numerators over the common denominator.
Step 6
Simplify each term.
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Step 6.1
Simplify the numerator.
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Step 6.1.1
Apply the distributive property.
Step 6.1.2
Apply the distributive property.
Step 6.1.3
Rewrite using the commutative property of multiplication.
Step 6.1.4
Multiply by .
Step 6.1.5
Subtract from .
Step 6.1.6
Add and .
Step 6.1.7
Factor out of .
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Step 6.1.7.1
Factor out of .
Step 6.1.7.2
Factor out of .
Step 6.1.7.3
Factor out of .
Step 6.2
Cancel the common factor of .
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Step 6.2.1
Cancel the common factor.
Step 6.2.2
Rewrite the expression.
Step 7
Simplify terms.
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Step 7.1
Reorder terms.
Step 7.2
Combine the numerators over the common denominator.
Step 7.3
Factor out of .
Step 7.4
Factor out of .
Step 7.5
Factor out of .
Step 7.6
Rewrite negatives.
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Step 7.6.1
Rewrite as .
Step 7.6.2
Move the negative in front of the fraction.