Trigonometry Examples

Simplify (d^2+d-30)/(d^2+3d-40)+(d^2+14d+48)/(d^2-2d-48)
Step 1
Simplify each term.
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Step 1.1
Factor using the AC method.
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Step 1.1.1
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 1.1.2
Write the factored form using these integers.
Step 1.2
Factor using the AC method.
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Step 1.2.1
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 1.2.2
Write the factored form using these integers.
Step 1.3
Cancel the common factor of .
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Step 1.3.1
Cancel the common factor.
Step 1.3.2
Rewrite the expression.
Step 1.4
Factor using the AC method.
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Step 1.4.1
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 1.4.2
Write the factored form using these integers.
Step 1.5
Factor using the AC method.
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Step 1.5.1
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 1.5.2
Write the factored form using these integers.
Step 1.6
Cancel the common factor of .
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Step 1.6.1
Cancel the common factor.
Step 1.6.2
Rewrite the expression.
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 5
Combine the numerators over the common denominator.
Step 6
Simplify the numerator.
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Step 6.1
Expand using the FOIL Method.
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Step 6.1.1
Apply the distributive property.
Step 6.1.2
Apply the distributive property.
Step 6.1.3
Apply the distributive property.
Step 6.2
Simplify and combine like terms.
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Step 6.2.1
Simplify each term.
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Step 6.2.1.1
Multiply by .
Step 6.2.1.2
Move to the left of .
Step 6.2.1.3
Multiply by .
Step 6.2.2
Add and .
Step 6.3
Expand using the FOIL Method.
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Step 6.3.1
Apply the distributive property.
Step 6.3.2
Apply the distributive property.
Step 6.3.3
Apply the distributive property.
Step 6.4
Simplify and combine like terms.
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Step 6.4.1
Simplify each term.
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Step 6.4.1.1
Multiply by .
Step 6.4.1.2
Move to the left of .
Step 6.4.1.3
Multiply by .
Step 6.4.2
Add and .
Step 6.5
Add and .
Step 6.6
Add and .
Step 6.7
Add and .
Step 6.8
Factor out of .
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Step 6.8.1
Factor out of .
Step 6.8.2
Factor out of .
Step 6.8.3
Factor out of .
Step 6.8.4
Factor out of .
Step 6.8.5
Factor out of .