Basic Math Examples

Simplify (5 square root of c+2)/(3+ square root of c)
Step 1
Multiply by .
Step 2
Combine fractions.
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Step 2.1
Multiply by .
Step 2.2
Expand the denominator using the FOIL method.
Step 2.3
Simplify.
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Step 2.3.1
Use to rewrite as .
Step 2.3.2
Apply the power rule and multiply exponents, .
Step 2.3.3
Combine and .
Step 2.3.4
Cancel the common factor of .
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Step 2.3.4.1
Cancel the common factor.
Step 2.3.4.2
Rewrite the expression.
Step 2.3.5
Simplify.
Step 3
Expand using the FOIL Method.
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Step 3.1
Apply the distributive property.
Step 3.2
Apply the distributive property.
Step 3.3
Apply the distributive property.
Step 4
Simplify and combine like terms.
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Step 4.1
Simplify each term.
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Step 4.1.1
Multiply by .
Step 4.1.2
Multiply .
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Step 4.1.2.1
Multiply by .
Step 4.1.2.2
Raise to the power of .
Step 4.1.2.3
Raise to the power of .
Step 4.1.2.4
Use the power rule to combine exponents.
Step 4.1.2.5
Add and .
Step 4.1.3
Rewrite as .
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Step 4.1.3.1
Use to rewrite as .
Step 4.1.3.2
Apply the power rule and multiply exponents, .
Step 4.1.3.3
Combine and .
Step 4.1.3.4
Cancel the common factor of .
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Step 4.1.3.4.1
Cancel the common factor.
Step 4.1.3.4.2
Rewrite the expression.
Step 4.1.3.5
Simplify.
Step 4.1.4
Multiply by .
Step 4.1.5
Multiply by .
Step 4.2
Subtract from .
Step 5
Simplify the numerator.
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Step 5.1
Use to rewrite as .
Step 5.2
Reorder terms.
Step 5.3
Rewrite in a factored form.
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Step 5.3.1
Rewrite as .
Step 5.3.2
Let . Substitute for all occurrences of .
Step 5.3.3
Factor by grouping.
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Step 5.3.3.1
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 5.3.3.1.1
Factor out of .
Step 5.3.3.1.2
Rewrite as plus
Step 5.3.3.1.3
Apply the distributive property.
Step 5.3.3.2
Factor out the greatest common factor from each group.
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Step 5.3.3.2.1
Group the first two terms and the last two terms.
Step 5.3.3.2.2
Factor out the greatest common factor (GCF) from each group.
Step 5.3.3.3
Factor the polynomial by factoring out the greatest common factor, .
Step 5.3.4
Replace all occurrences of with .
Step 5.3.5
Factor out of .
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Step 5.3.5.1
Factor out of .
Step 5.3.5.2
Rewrite as .
Step 5.3.5.3
Factor out of .
Step 6
Move the negative in front of the fraction.