Finite Math Examples

Simplify (9a^2)/((3-a)^2)-1(a/(a-3)+(12a^2-9a)/(27-a^3)+9/(a^2+3a+9))
Step 1
Simplify each term.
Tap for more steps...
Step 1.1
Simplify each term.
Tap for more steps...
Step 1.1.1
Factor out of .
Tap for more steps...
Step 1.1.1.1
Factor out of .
Step 1.1.1.2
Factor out of .
Step 1.1.1.3
Factor out of .
Step 1.1.2
Simplify the denominator.
Tap for more steps...
Step 1.1.2.1
Rewrite as .
Step 1.1.2.2
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Step 1.1.2.3
Raise to the power of .
Step 1.2
Rewrite as .
Step 1.3
Factor out of .
Step 1.4
Factor out of .
Step 1.5
Move a negative from the denominator of to the numerator.
Step 1.6
Reorder terms.
Step 1.7
To write as a fraction with a common denominator, multiply by .
Step 1.8
Multiply by .
Step 1.9
Combine the numerators over the common denominator.
Step 1.10
Simplify each term.
Tap for more steps...
Step 1.10.1
Simplify the numerator.
Tap for more steps...
Step 1.10.1.1
Factor out of .
Tap for more steps...
Step 1.10.1.1.1
Factor out of .
Step 1.10.1.1.2
Factor out of .
Step 1.10.1.2
Multiply by .
Step 1.10.1.3
Apply the distributive property.
Step 1.10.1.4
Multiply by .
Step 1.10.1.5
Multiply by .
Step 1.10.1.6
Add and .
Step 1.10.1.7
Subtract from .
Step 1.10.1.8
Factor using the AC method.
Tap for more steps...
Step 1.10.1.8.1
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 1.10.1.8.2
Write the factored form using these integers.
Step 1.10.2
Cancel the common factor of .
Tap for more steps...
Step 1.10.2.1
Cancel the common factor.
Step 1.10.2.2
Rewrite the expression.
Step 1.11
Reorder terms.
Step 1.12
Combine the numerators over the common denominator.
Step 1.13
Simplify the numerator.
Tap for more steps...
Step 1.13.1
Apply the distributive property.
Step 1.13.2
Multiply by .
Step 1.13.3
Move to the left of .
Step 1.13.4
Factor using the perfect square rule.
Tap for more steps...
Step 1.13.4.1
Rewrite as .
Step 1.13.4.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 1.13.4.3
Rewrite the polynomial.
Step 1.13.4.4
Factor using the perfect square trinomial rule , where and .
Step 1.14
Rewrite as .
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 .
Tap for more steps...
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.
Tap for more steps...
Step 6.1
Apply the distributive property.
Step 6.2
Simplify.
Tap for more steps...
Step 6.2.1
Multiply by by adding the exponents.
Tap for more steps...
Step 6.2.1.1
Move .
Step 6.2.1.2
Use the power rule to combine exponents.
Step 6.2.1.3
Add and .
Step 6.2.2
Rewrite using the commutative property of multiplication.
Step 6.2.3
Multiply by .
Step 6.3
Simplify each term.
Tap for more steps...
Step 6.3.1
Multiply by by adding the exponents.
Tap for more steps...
Step 6.3.1.1
Move .
Step 6.3.1.2
Multiply by .
Tap for more steps...
Step 6.3.1.2.1
Raise to the power of .
Step 6.3.1.2.2
Use the power rule to combine exponents.
Step 6.3.1.3
Add and .
Step 6.3.2
Multiply by .
Step 6.4
Rewrite as .
Step 6.5
Expand using the FOIL Method.
Tap for more steps...
Step 6.5.1
Apply the distributive property.
Step 6.5.2
Apply the distributive property.
Step 6.5.3
Apply the distributive property.
Step 6.6
Simplify and combine like terms.
Tap for more steps...
Step 6.6.1
Simplify each term.
Tap for more steps...
Step 6.6.1.1
Multiply by .
Step 6.6.1.2
Move to the left of .
Step 6.6.1.3
Multiply by .
Step 6.6.2
Subtract from .
Step 6.7
Apply the distributive property.
Step 6.8
Simplify.
Tap for more steps...
Step 6.8.1
Multiply by .
Step 6.8.2
Multiply by .
Step 6.9
Rewrite as .
Step 6.10
Expand using the FOIL Method.
Tap for more steps...
Step 6.10.1
Apply the distributive property.
Step 6.10.2
Apply the distributive property.
Step 6.10.3
Apply the distributive property.
Step 6.11
Simplify and combine like terms.
Tap for more steps...
Step 6.11.1
Simplify each term.
Tap for more steps...
Step 6.11.1.1
Multiply by .
Step 6.11.1.2
Multiply by .
Step 6.11.1.3
Multiply by .
Step 6.11.1.4
Rewrite using the commutative property of multiplication.
Step 6.11.1.5
Multiply by by adding the exponents.
Tap for more steps...
Step 6.11.1.5.1
Move .
Step 6.11.1.5.2
Multiply by .
Step 6.11.1.6
Multiply by .
Step 6.11.1.7
Multiply by .
Step 6.11.2
Subtract from .
Step 6.12
Expand by multiplying each term in the first expression by each term in the second expression.
Step 6.13
Simplify each term.
Tap for more steps...
Step 6.13.1
Multiply by .
Step 6.13.2
Rewrite using the commutative property of multiplication.
Step 6.13.3
Multiply by by adding the exponents.
Tap for more steps...
Step 6.13.3.1
Move .
Step 6.13.3.2
Multiply by .
Tap for more steps...
Step 6.13.3.2.1
Raise to the power of .
Step 6.13.3.2.2
Use the power rule to combine exponents.
Step 6.13.3.3
Add and .
Step 6.13.4
Multiply by .
Step 6.13.5
Multiply by by adding the exponents.
Tap for more steps...
Step 6.13.5.1
Move .
Step 6.13.5.2
Use the power rule to combine exponents.
Step 6.13.5.3
Add and .
Step 6.13.6
Multiply by .
Step 6.13.7
Rewrite using the commutative property of multiplication.
Step 6.13.8
Multiply by by adding the exponents.
Tap for more steps...
Step 6.13.8.1
Move .
Step 6.13.8.2
Multiply by .
Step 6.13.9
Multiply by .
Step 6.13.10
Multiply by by adding the exponents.
Tap for more steps...
Step 6.13.10.1
Move .
Step 6.13.10.2
Multiply by .
Tap for more steps...
Step 6.13.10.2.1
Raise to the power of .
Step 6.13.10.2.2
Use the power rule to combine exponents.
Step 6.13.10.3
Add and .
Step 6.13.11
Multiply by .
Step 6.13.12
Multiply by .
Step 6.14
Subtract from .
Step 6.15
Add and .
Step 6.16
Add and .
Step 6.17
Subtract from .
Step 6.18
Subtract from .
Step 6.19
Add and .
Step 6.20
Subtract from .