Factor (3a)/(a^2-9)-(2b)/(ab+3b)-b/(ab-3b)

Math
3aa2-9-2bab+3b-bab-3b
Factor b out of ab+3b.
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Factor b out of ab.
3aa2-9-2bba+3b-bab-3b
Factor b out of 3b.
3aa2-9-2bba+b⋅3-bab-3b
Factor b out of ba+b⋅3.
3aa2-9-2bb(a+3)-bab-3b
3aa2-9-2bb(a+3)-bab-3b
Cancel the common factor of b.
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Cancel the common factor.
3aa2-9-2bb(a+3)-bab-3b
Rewrite the expression.
3aa2-9-2a+3-bab-3b
3aa2-9-2a+3-bab-3b
Factor b out of ab-3b.
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Factor b out of ab.
3aa2-9-2a+3-bba-3b
Factor b out of -3b.
3aa2-9-2a+3-bba+b⋅-3
Factor b out of ba+b⋅-3.
3aa2-9-2a+3-bb(a-3)
3aa2-9-2a+3-bb(a-3)
Cancel the common factor of b.
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Cancel the common factor.
3aa2-9-2a+3-bb(a-3)
Rewrite the expression.
3aa2-9-2a+3-1a-3
3aa2-9-2a+3-1a-3
To write 3aa2-9 as a fraction with a common denominator, multiply by a+3a+3.
3aa2-9⋅a+3a+3-2a+3-1a-3
To write -2a+3 as a fraction with a common denominator, multiply by a2-9a2-9.
3aa2-9⋅a+3a+3-2a+3⋅a2-9a2-9-1a-3
Write each expression with a common denominator of (a2-9)(a+3), by multiplying each by an appropriate factor of 1.
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Multiply 3aa2-9 and a+3a+3.
3a(a+3)(a2-9)(a+3)-2a+3⋅a2-9a2-9-1a-3
Multiply 2a+3 and a2-9a2-9.
3a(a+3)(a2-9)(a+3)-2(a2-9)(a+3)(a2-9)-1a-3
Reorder the factors of (a2-9)(a+3).
3a(a+3)(a+3)(a2-9)-2(a2-9)(a+3)(a2-9)-1a-3
3a(a+3)(a+3)(a2-9)-2(a2-9)(a+3)(a2-9)-1a-3
Combine the numerators over the common denominator.
3a(a+3)-2(a2-9)(a+3)(a2-9)-1a-3
To write 3a(a+3)-2(a2-9)(a+3)(a2-9) as a fraction with a common denominator, multiply by a-3a-3.
3a(a+3)-2(a2-9)(a+3)(a2-9)⋅a-3a-3-1a-3
To write -1a-3 as a fraction with a common denominator, multiply by (a+3)(a2-9)(a+3)(a2-9).
3a(a+3)-2(a2-9)(a+3)(a2-9)⋅a-3a-3-1a-3⋅(a+3)(a2-9)(a+3)(a2-9)
Write each expression with a common denominator of (a+3)(a2-9)(a-3), by multiplying each by an appropriate factor of 1.
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Multiply 3a(a+3)-2(a2-9)(a+3)(a2-9) and a-3a-3.
(3a(a+3)-2(a2-9))(a-3)(a+3)(a2-9)(a-3)-1a-3⋅(a+3)(a2-9)(a+3)(a2-9)
Multiply 1a-3 and (a+3)(a2-9)(a+3)(a2-9).
(3a(a+3)-2(a2-9))(a-3)(a+3)(a2-9)(a-3)-(a+3)(a2-9)(a-3)((a+3)(a2-9))
Reorder the factors of (a+3)(a2-9)(a-3).
(3a(a+3)-2(a2-9))(a-3)(a+3)(a-3)(a2-9)-(a+3)(a2-9)(a-3)((a+3)(a2-9))
Reorder the factors of (a-3)((a+3)(a2-9)).
(3a(a+3)-2(a2-9))(a-3)(a+3)(a-3)(a2-9)-(a+3)(a2-9)(a+3)(a-3)(a2-9)
(3a(a+3)-2(a2-9))(a-3)(a+3)(a-3)(a2-9)-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Combine the numerators over the common denominator.
(3a(a+3)-2(a2-9))(a-3)-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Rewrite (3a(a+3)-2(a2-9))(a-3)-(a+3)(a2-9)(a+3)(a-3)(a2-9) in a factored form.
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Simplify each term.
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Apply the distributive property.
(3a⋅a+3a⋅3-2(a2-9))(a-3)-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Multiply a by a by adding the exponents.
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Move a.
(3(a⋅a)+3a⋅3-2(a2-9))(a-3)-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Multiply a by a.
(3a2+3a⋅3-2(a2-9))(a-3)-(a+3)(a2-9)(a+3)(a-3)(a2-9)
(3a2+3a⋅3-2(a2-9))(a-3)-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Multiply 3 by 3.
(3a2+9a-2(a2-9))(a-3)-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Apply the distributive property.
(3a2+9a-2a2-2⋅-9)(a-3)-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Multiply -2 by -9.
(3a2+9a-2a2+18)(a-3)-(a+3)(a2-9)(a+3)(a-3)(a2-9)
(3a2+9a-2a2+18)(a-3)-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Subtract 2a2 from 3a2.
(a2+9a+18)(a-3)-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Expand (a2+9a+18)(a-3) by multiplying each term in the first expression by each term in the second expression.
a2a+a2⋅-3+9a⋅a+9a⋅-3+18a+18⋅-3-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Simplify each term.
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Multiply a2 by a by adding the exponents.
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Multiply a2 by a.
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Raise a to the power of 1.
a2a1+a2⋅-3+9a⋅a+9a⋅-3+18a+18⋅-3-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Use the power rule aman=am+n to combine exponents.
a2+1+a2⋅-3+9a⋅a+9a⋅-3+18a+18⋅-3-(a+3)(a2-9)(a+3)(a-3)(a2-9)
a2+1+a2⋅-3+9a⋅a+9a⋅-3+18a+18⋅-3-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Add 2 and 1.
a3+a2⋅-3+9a⋅a+9a⋅-3+18a+18⋅-3-(a+3)(a2-9)(a+3)(a-3)(a2-9)
a3+a2⋅-3+9a⋅a+9a⋅-3+18a+18⋅-3-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Move -3 to the left of a2.
a3-3a2+9a⋅a+9a⋅-3+18a+18⋅-3-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Multiply a by a by adding the exponents.
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Move a.
a3-3a2+9(a⋅a)+9a⋅-3+18a+18⋅-3-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Multiply a by a.
a3-3a2+9a2+9a⋅-3+18a+18⋅-3-(a+3)(a2-9)(a+3)(a-3)(a2-9)
a3-3a2+9a2+9a⋅-3+18a+18⋅-3-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Multiply -3 by 9.
a3-3a2+9a2-27a+18a+18⋅-3-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Multiply 18 by -3.
a3-3a2+9a2-27a+18a-54-(a+3)(a2-9)(a+3)(a-3)(a2-9)
a3-3a2+9a2-27a+18a-54-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Add -3a2 and 9a2.
a3+6a2-27a+18a-54-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Add -27a and 18a.
a3+6a2-9a-54-(a+3)(a2-9)(a+3)(a-3)(a2-9)
Apply the distributive property.
a3+6a2-9a-54+(-a-1⋅3)(a2-9)(a+3)(a-3)(a2-9)
Multiply -1 by 3.
a3+6a2-9a-54+(-a-3)(a2-9)(a+3)(a-3)(a2-9)
Expand (-a-3)(a2-9) using the FOIL Method.
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Apply the distributive property.
a3+6a2-9a-54-a(a2-9)-3(a2-9)(a+3)(a-3)(a2-9)
Apply the distributive property.
a3+6a2-9a-54-a⋅a2-a⋅-9-3(a2-9)(a+3)(a-3)(a2-9)
Apply the distributive property.
a3+6a2-9a-54-a⋅a2-a⋅-9-3a2-3⋅-9(a+3)(a-3)(a2-9)
a3+6a2-9a-54-a⋅a2-a⋅-9-3a2-3⋅-9(a+3)(a-3)(a2-9)
Simplify each term.
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Multiply a by a2 by adding the exponents.
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Move a2.
a3+6a2-9a-54-(a2a)-a⋅-9-3a2-3⋅-9(a+3)(a-3)(a2-9)
Multiply a2 by a.
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Raise a to the power of 1.
a3+6a2-9a-54-(a2a1)-a⋅-9-3a2-3⋅-9(a+3)(a-3)(a2-9)
Use the power rule aman=am+n to combine exponents.
a3+6a2-9a-54-a2+1-a⋅-9-3a2-3⋅-9(a+3)(a-3)(a2-9)
a3+6a2-9a-54-a2+1-a⋅-9-3a2-3⋅-9(a+3)(a-3)(a2-9)
Add 2 and 1.
a3+6a2-9a-54-a3-a⋅-9-3a2-3⋅-9(a+3)(a-3)(a2-9)
a3+6a2-9a-54-a3-a⋅-9-3a2-3⋅-9(a+3)(a-3)(a2-9)
Multiply -9 by -1.
a3+6a2-9a-54-a3+9a-3a2-3⋅-9(a+3)(a-3)(a2-9)
Multiply -3 by -9.
a3+6a2-9a-54-a3+9a-3a2+27(a+3)(a-3)(a2-9)
a3+6a2-9a-54-a3+9a-3a2+27(a+3)(a-3)(a2-9)
Subtract a3 from a3.
6a2-9a-54+0+9a-3a2+27(a+3)(a-3)(a2-9)
Add 6a2 and 0.
6a2-9a-54+9a-3a2+27(a+3)(a-3)(a2-9)
Subtract 3a2 from 6a2.
3a2-9a-54+9a+27(a+3)(a-3)(a2-9)
Add -9a and 9a.
3a2+0-54+27(a+3)(a-3)(a2-9)
Add 3a2 and 0.
3a2-54+27(a+3)(a-3)(a2-9)
Add -54 and 27.
3a2-27(a+3)(a-3)(a2-9)
Rewrite 3a2-27 in a factored form.
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Factor 3 out of 3a2-27.
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Factor 3 out of 3a2.
3(a2)-27(a+3)(a-3)(a2-9)
Factor 3 out of -27.
3a2+3⋅-9(a+3)(a-3)(a2-9)
Factor 3 out of 3a2+3⋅-9.
3(a2-9)(a+3)(a-3)(a2-9)
3(a2-9)(a+3)(a-3)(a2-9)
Rewrite 9 as 32.
3(a2-32)(a+3)(a-3)(a2-9)
Factor.
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Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a and b=3.
3((a+3)(a-3))(a+3)(a-3)(a2-9)
Remove unnecessary parentheses.
3(a+3)(a-3)(a+3)(a-3)(a2-9)
3(a+3)(a-3)(a+3)(a-3)(a2-9)
3(a+3)(a-3)(a+3)(a-3)(a2-9)
Rewrite 9 as 32.
3(a+3)(a-3)(a+3)(a-3)(a2-32)
Factor.
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Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a and b=3.
3(a+3)(a-3)(a+3)(a-3)((a+3)(a-3))
Remove unnecessary parentheses.
3(a+3)(a-3)(a+3)(a-3)(a+3)(a-3)
3(a+3)(a-3)(a+3)(a-3)(a+3)(a-3)
Combine exponents.
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Raise a+3 to the power of 1.
3(a+3)(a-3)(a+3)1(a+3)(a-3)(a-3)
Raise a+3 to the power of 1.
3(a+3)(a-3)(a+3)1(a+3)1(a-3)(a-3)
Use the power rule aman=am+n to combine exponents.
3(a+3)(a-3)(a+3)1+1(a-3)(a-3)
Add 1 and 1.
3(a+3)(a-3)(a+3)2(a-3)(a-3)
Raise a-3 to the power of 1.
3(a+3)(a-3)(a+3)2((a-3)1(a-3))
Raise a-3 to the power of 1.
3(a+3)(a-3)(a+3)2((a-3)1(a-3)1)
Use the power rule aman=am+n to combine exponents.
3(a+3)(a-3)(a+3)2(a-3)1+1
Add 1 and 1.
3(a+3)(a-3)(a+3)2(a-3)2
3(a+3)(a-3)(a+3)2(a-3)2
Reduce the expression 3(a+3)(a-3)(a+3)2(a-3)2 by cancelling the common factors.
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Factor a+3 out of 3(a+3)(a-3).
(a+3)(3(a-3))(a+3)2(a-3)2
Factor a+3 out of (a+3)2(a-3)2.
(a+3)(3(a-3))(a+3)((a+3)(a-3)2)
Cancel the common factor.
(a+3)(3(a-3))(a+3)((a+3)(a-3)2)
Rewrite the expression.
3(a-3)(a+3)(a-3)2
3(a-3)(a+3)(a-3)2
3(a-3)(a+3)(a-3)2
Reduce the expression 3(a-3)(a+3)(a-3)2 by cancelling the common factors.
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Factor a-3 out of 3(a-3).
(a-3)⋅3(a+3)(a-3)2
Factor a-3 out of (a+3)(a-3)2.
(a-3)⋅3(a-3)((a+3)(a-3))
Cancel the common factor.
(a-3)⋅3(a-3)((a+3)(a-3))
Rewrite the expression.
3(a+3)(a-3)
3(a+3)(a-3)
Factor (3a)/(a^2-9)-(2b)/(ab+3b)-b/(ab-3b)

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