Simplify a/(a-b)+6/(6-a)

Math
aa-b+66-a
To write aa-b as a fraction with a common denominator, multiply by 6-a6-a.
aa-b⋅6-a6-a+66-a
To write 66-a as a fraction with a common denominator, multiply by a-ba-b.
aa-b⋅6-a6-a+66-a⋅a-ba-b
Write each expression with a common denominator of (a-b)(6-a), by multiplying each by an appropriate factor of 1.
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Multiply aa-b and 6-a6-a.
a(6-a)(a-b)(6-a)+66-a⋅a-ba-b
Multiply 66-a and a-ba-b.
a(6-a)(a-b)(6-a)+6(a-b)(6-a)(a-b)
Reorder the factors of (a-b)(6-a).
a(6-a)(6-a)(a-b)+6(a-b)(6-a)(a-b)
a(6-a)(6-a)(a-b)+6(a-b)(6-a)(a-b)
Combine the numerators over the common denominator.
a(6-a)+6(a-b)(6-a)(a-b)
Simplify the numerator.
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Apply the distributive property.
a⋅6+a(-a)+6(a-b)(6-a)(a-b)
Move 6 to the left of a.
6⋅a+a(-a)+6(a-b)(6-a)(a-b)
Rewrite using the commutative property of multiplication.
6⋅a-a⋅a+6(a-b)(6-a)(a-b)
Multiply a by a by adding the exponents.
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Move a.
6a-(a⋅a)+6(a-b)(6-a)(a-b)
Multiply a by a.
6a-a2+6(a-b)(6-a)(a-b)
6a-a2+6(a-b)(6-a)(a-b)
Apply the distributive property.
6a-a2+6a+6(-b)(6-a)(a-b)
Multiply -1 by 6.
6a-a2+6a-6b(6-a)(a-b)
Add 6a and 6a.
-a2+12a-6b(6-a)(a-b)
-a2+12a-6b(6-a)(a-b)
Simplify with factoring out.
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Factor -1 out of -a2.
-(a2)+12a-6b(6-a)(a-b)
Factor -1 out of 12a.
-(a2)-(-12a)-6b(6-a)(a-b)
Factor -1 out of -(a2)-(-12a).
-(a2-12a)-6b(6-a)(a-b)
Factor -1 out of -6b.
-(a2-12a)-(6b)(6-a)(a-b)
Factor -1 out of -(a2-12a)-(6b).
-(a2-12a+6b)(6-a)(a-b)
Simplify the expression.
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Rewrite -(a2-12a+6b) as -1(a2-12a+6b).
-1(a2-12a+6b)(6-a)(a-b)
Move the negative in front of the fraction.
-a2-12a+6b(6-a)(a-b)
-a2-12a+6b(6-a)(a-b)
-a2-12a+6b(6-a)(a-b)
Simplify a/(a-b)+6/(6-a)

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