Pre-Algebra Examples

Divide (-7 square root of x-5)/( square root of x+9)
Step 1
Factor out of .
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Step 1.1
Factor out of .
Step 1.2
Rewrite as .
Step 1.3
Factor out of .
Step 2
Move the negative in front of the fraction.
Step 3
Multiply by .
Step 4
Multiply by .
Step 5
Expand the denominator using the FOIL method.
Step 6
Simplify.
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Step 6.1
Use to rewrite as .
Step 6.2
Apply the power rule and multiply exponents, .
Step 6.3
Combine and .
Step 6.4
Cancel the common factor of .
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Step 6.4.1
Cancel the common factor.
Step 6.4.2
Rewrite the expression.
Step 6.5
Simplify.
Step 7
Expand using the FOIL Method.
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Step 7.1
Apply the distributive property.
Step 7.2
Apply the distributive property.
Step 7.3
Apply the distributive property.
Step 8
Simplify and combine like terms.
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Step 8.1
Simplify each term.
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Step 8.1.1
Multiply .
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Step 8.1.1.1
Raise to the power of .
Step 8.1.1.2
Raise to the power of .
Step 8.1.1.3
Use the power rule to combine exponents.
Step 8.1.1.4
Add and .
Step 8.1.2
Rewrite as .
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Step 8.1.2.1
Use to rewrite as .
Step 8.1.2.2
Apply the power rule and multiply exponents, .
Step 8.1.2.3
Combine and .
Step 8.1.2.4
Cancel the common factor of .
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Step 8.1.2.4.1
Cancel the common factor.
Step 8.1.2.4.2
Rewrite the expression.
Step 8.1.2.5
Simplify.
Step 8.1.3
Multiply by .
Step 8.1.4
Multiply by .
Step 8.2
Add and .
Step 9
Simplify the numerator.
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Step 9.1
Use to rewrite as .
Step 9.2
Rewrite as .
Step 9.3
Let . Substitute for all occurrences of .
Step 9.4
Factor by grouping.
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Step 9.4.1
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 9.4.1.1
Factor out of .
Step 9.4.1.2
Rewrite as plus
Step 9.4.1.3
Apply the distributive property.
Step 9.4.2
Factor out the greatest common factor from each group.
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Step 9.4.2.1
Group the first two terms and the last two terms.
Step 9.4.2.2
Factor out the greatest common factor (GCF) from each group.
Step 9.4.3
Factor the polynomial by factoring out the greatest common factor, .
Step 9.5
Replace all occurrences of with .
Step 10
Expand using the FOIL Method.
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Step 10.1
Apply the distributive property.
Step 10.2
Apply the distributive property.
Step 10.3
Apply the distributive property.
Step 11
Simplify and combine like terms.
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Step 11.1
Simplify each term.
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Step 11.1.1
Multiply by by adding the exponents.
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Step 11.1.1.1
Move .
Step 11.1.1.2
Use the power rule to combine exponents.
Step 11.1.1.3
Combine the numerators over the common denominator.
Step 11.1.1.4
Add and .
Step 11.1.1.5
Divide by .
Step 11.1.2
Simplify .
Step 11.1.3
Multiply by .
Step 11.1.4
Multiply by .
Step 11.2
Add and .
Step 12
Split the fraction into two fractions.
Step 13
Split the fraction into two fractions.
Step 14
Move the negative in front of the fraction.
Step 15
Move the negative in front of the fraction.