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Suppose $$\frac{2(1-2x)}{x^2-x-2} = \frac{A}{x-2} + \frac{B}{x+1}$$

How can I get the value of $A+B$ for my math exam?

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For this question to have an answer, it should be supposed that $x$ is an unknown. Notice that $x^2 - x -2 = (x-2)(x +1)$. So, what will you get if you multiply both sides by $(x-2)(x+1)$? Try to get an equation of the form $(\cdot)x + (\cdot) = 0$. Then the things in the $()$'s must both be $0$ for the equation to hold. You know how to do it now? – ShinyaSakai Nov 13 '11 at 16:56
If it helps, here you can find a few solved exercises of this type: – Martin Sleziak Nov 13 '11 at 17:36
up vote 0 down vote accepted

This should help. $$ 2 - 4x = Ax + A + Bx - 2B = (A+B) x + (A-2B)$$

Compare coefficients.

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I'm a student.What is the result difficult to understand? – Yusuf Ali Bozkır Nov 13 '11 at 16:42
@Yusuf It's not clear what you mean. Do you want an elaboration of the answer? Which part do you not follow? – Srivatsan Nov 13 '11 at 17:04

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