Question

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The equation
24x2+25x−47
ax−2
=−8x−3−
53
ax−2
is true for all values of x≠
2
a
, where a is a constant.

What is the value of a?​

Answer 1

multiply both side of given equation by ax-2 . when you multiply each side by ax-2 you should have:

24×2+25×-47=(-8×-3)(ax-2)-53

you should than multiply (-8×-3) and (ax-2) using FOIL.

24×2+25×-47= -8ax2-3ax+16×+6-53

Then,reduce on the right side of the equation

24×2+25×-47=-8ax2-3ax+16×-47

Since the coefficient of the x2- term have to be equal on the both sides of the equation ,

-8a=24,or a = -3

So the value of a is -3

Answer is -3