# Answer to Question #28412 in Algebra for IKIN

Question #28412

1/3 (6ab-5ab)-1/6(2b-12)

Expert's answer

we know that for every x, a,b ax+bx=(a+b)x then (6ab-5ab)=(6-5)ab =1*ab=abalso (2b-12)=(b-6)*2

hence 1/3 (6ab-5ab)=1/3 *ab=ab/31/6(2b-12)=2(b-6)/6=(b-6)/3

so we obtain

1/3 (6ab-5ab)-1/6(2b-12)=ab/3 -(b-6)/3

(b-6)/3=b/3-6/3=b/3-2

ab/3 -(b-6)/3=ab/3 -(b/3 -2)

-(b/3-2)=-b/3+2

Therefore, ab/3 -(b/3-2)=ab/3-b/3+2=(a-1)*b/3 +2 The result is (a-1)*b/3+2

hence 1/3 (6ab-5ab)=1/3 *ab=ab/31/6(2b-12)=2(b-6)/6=(b-6)/3

so we obtain

1/3 (6ab-5ab)-1/6(2b-12)=ab/3 -(b-6)/3

(b-6)/3=b/3-6/3=b/3-2

ab/3 -(b-6)/3=ab/3 -(b/3 -2)

-(b/3-2)=-b/3+2

Therefore, ab/3 -(b/3-2)=ab/3-b/3+2=(a-1)*b/3 +2 The result is (a-1)*b/3+2

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