The equation 24x2+25x−47ax−2=−8x−3−53ax−2 is true for all values of x≠2a, where a is a constant.
What is the value of a?
There are two ways to solve this question. The faster way is to 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:
You should then multiply (−8x−3) and (ax−2) using FOIL.
Then, reduce on the right side of the equation
Since the coefficients of the x2-term have to be equal on both sides of the equation, −8a=24, or a=−3.