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# help with algebra

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There are real numbers A and B such that

(5x + 16)/(x^2 - 7x + 10) = A/(x - 2) + B/(x - 5).

Find A + B.

Jul 7, 2021

#1
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We can start off by multiplying $$x^2-7x+10$$ on both sides which cancels out the denominators.

$$5x+16 = A \cdot (x-5) + B \cdot (x-2) \\ 5x+16 = Ax-5A + Bx-2B \\ 5x+16 = (A+B)x - 5A - 2B$$

Because -5A-2B will not result in something in terms of x, we can ignore it and 16. So we are left with,

$$5x = (A+B)x \\ A+B = 5$$

So A+B = 5.

Jul 7, 2021
#2
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I really liked your matching-up with constants and variables! +1

#3
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Thanks!!

Awesomeguy  Jul 7, 2021