math

Let $A$ and $B$ be real numbers such that
$\frac{A}{x-5}+B(x+1)=\frac{-3x^2+12x+22}{x-5}$. What is $A+B$?

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  1. It is so easy to write a fraction as 4/5 for "four over five"

    so I will interpret your gibberish as
    A(x-5) + B(x+1) = (-3x^2 + 12x + 22)/(x-5)

    confirm if that is what you meant before I start my answer.

  2. Input it into a latex converter, and u will get your thing

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    posted by Charles
  3. It appears you meant
    A/(x-5) + B(x+1) = (-3x^2 + 12x + 22)/(x-5)
    If so, then
    A + B(x+1)(x-5) = -3x^2 + 12x + 22
    Now just expand the left side, and make sure coefficients of like exponents are the same. That gives you
    Bx^2 - 4Bx - 5B+A = -3x^2 + 12x + 22
    B = -3
    -4B = 12 (good thing that's consistent!)
    -5B+A = 22
    Now just find A, and then A+B

    This is clearly not a TeX- friendly forum. Henceforth, just use plain text.

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