24x2+ 25x − 47 divided by ax − 2 is equal to
−8x −3 with remainder −53, it is true that (−8x − 3)(ax − 2) − 53 = 24x2 +25x −47. (This can be seen by multiplying each side of the given equation by

ax − 2). This can be rewritten as −8ax2+ 16x − 3ax = 24x2+ 25x − 47.

Since
the coefficients of the x2
-term have to be equal on both sides of the equation,
−8a = 24, or a = −3.

by Level 12 User (101k points)
selected

I guess (24x^2 + 25x - 47)/(ax-2) = -8x - 3 - (53/(ax-2)) is the intended question. This would imply that -8ax^2=24x^2 making -8a=24, a=-3, just by balancing the x^2 term. Assuming this initially, let's see the result of multiplying through by -(3x+2):

24x^2+25x-47=-(3x+2)(-8x-3)-53=(3x+2)(8x+3)-53=24x^2+25x+6-53=24x^2+25x-47. The equation is an identity, thus proving a=-3 is the solution for all x≠2/a or x≠-2/3 (which would cause division by zero).

by Top Rated User (775k points)
multiply both sides of the given equation by ax−2. When you multiply each side by ax−2, you should have:

24x2+25x−47=(−8x−3)(ax−2)−53

You should then multiply (−8x−3) and (ax−2) using FOIL.

24x2+25x−47=−8ax2−3ax+16x+6−53

Then, reduce on the right side of the equation

24x2+25x−47=−8ax2−3ax+16x−47

Since the coefficients of the x2-term have to be equal on both sides of the equation, −8a=24, or a=−3.

hope u help dear..
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