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# need help with a quick problem

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If $$\displaystyle \frac{4x + 13}{(x - 2)(x + 1)} = \frac{A}{x - 2} + \frac{B}{x + 1}$$ for all x other than 2 and -1, then what are A and B?

Jul 11, 2020

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cross multipy the R side to get   [ a(x+1)  + b(x-2) ] / [(x-2)(x+1) ]

Now you can equate the numerators of both sides of the equation

4x+13 = ax+a   + bx-2b        and now you can equate   the 'x' components coefficient and the constant

4 = a+b

13 = a-2b

solve the simple system of red equations to find      a = 7 and   b = -3

Jul 11, 2020