The equation 24x^2 + 25x - 47/ax -2 = -8x -3-53/ax-2 is true for all values of x not equals to 2/a , where a is a constant . what is the value of a ?
A) -16
B) -3
C) 3
D) 16
please answer my query and explain it too how you got that answer
A) -16
B) -3
C) 3
D) 16
please answer my query and explain it too how you got that answer
Answers & Comments
Answer:
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:
24x^2+25x−47=(−8x−3)(ax−2)−53
You should then multiply (−8x−3) and (ax−2) using FOIL.
24x^2+25x−47=−8ax^2−3ax+16x+6−53
Then, reduce on the right side of the equation
24x^2+25x−47=−8ax^2−3ax+16x−47
Since the coefficients of the x2-term have to be equal on both sides of the equation, −8a=24, or a=−3.
The other option which is longer and more tedious is to attempt to plug in all of the answer choices for a and see which answer choice makes both sides of the equation equal. Again, this is the longer option, and I do not recommend it for the actual SAT as it will waste too much time.
The final answer is B.