Question

if x/(x-1)(x-2)=(A/x-1)+(B/x-2)​

Answer 1

Answer:

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Answer 2

A=-1 and B=2 (ANSWER)

⇒x/(x-1)(x-2)=(A/x-1)+(B/x-2)

⇒We can compare both sides of the equation and solve for A and B,

⇒x/(x-1)(x-2)=(A(x-2)+B(x-1))/(x-1)(x-2)

⇒x/(x-1)(x-2)=((A+B)x-(2A+B))/(x-1)(x-2)

comparing both sides we get,

A+B=1

2A+B=0

On solving both equations, A=-1,B=2 (ANSWER)