Basic Math Examples

Simplify (18/(h-9)+h/(h-5))/(4/(h-10)-3/(h-9))
Step 1
Multiply the numerator and denominator of the fraction by .
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Step 1.1
Multiply by .
Step 1.2
Combine.
Step 2
Apply the distributive property.
Step 3
Simplify by cancelling.
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Step 3.1
Cancel the common factor of .
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Step 3.1.1
Factor out of .
Step 3.1.2
Cancel the common factor.
Step 3.1.3
Rewrite the expression.
Step 3.2
Cancel the common factor of .
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Step 3.2.1
Factor out of .
Step 3.2.2
Cancel the common factor.
Step 3.2.3
Rewrite the expression.
Step 3.3
Cancel the common factor of .
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Step 3.3.1
Factor out of .
Step 3.3.2
Cancel the common factor.
Step 3.3.3
Rewrite the expression.
Step 3.4
Cancel the common factor of .
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Step 3.4.1
Move the leading negative in into the numerator.
Step 3.4.2
Factor out of .
Step 3.4.3
Cancel the common factor.
Step 3.4.4
Rewrite the expression.
Step 4
Simplify the numerator.
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Step 4.1
Factor out of .
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Step 4.1.1
Factor out of .
Step 4.1.2
Factor out of .
Step 4.1.3
Factor out of .
Step 4.2
Apply the distributive property.
Step 4.3
Move to the left of .
Step 4.4
Multiply by .
Step 4.5
Apply the distributive property.
Step 4.6
Multiply by .
Step 4.7
Subtract from .
Step 4.8
Reorder terms.
Step 4.9
Factor using the AC method.
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Step 4.9.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 4.9.2
Write the factored form using these integers.
Step 5
Simplify the denominator.
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Step 5.1
Factor out of .
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Step 5.1.1
Factor out of .
Step 5.1.2
Factor out of .
Step 5.1.3
Factor out of .
Step 5.2
Apply the distributive property.
Step 5.3
Move to the left of .
Step 5.4
Multiply by .
Step 5.5
Apply the distributive property.
Step 5.6
Move to the left of .
Step 5.7
Multiply by .
Step 5.8
Subtract from .
Step 5.9
Add and .
Step 6
Cancel the common factor of .
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Step 6.1
Cancel the common factor.
Step 6.2
Rewrite the expression.