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Algebra Level 3

$\large \frac {24x^2+25x-47}{ax-2} = -8x-3-\frac {53}{ax-2}$

The equation above is true for all $x \ne \dfrac 2a$ , where $a$ is a constant. What is the value of $a$ ?

1 solution

Abhyudaya Apoorva
Dec 28, 2016

Multiply each side of the given equation by ax−2 (so you can get rid of the fraction). 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.