Question

Please please help!! I have no clue how to do this!!

Answer 1

The LCD here is ax-2. Let's try to eliminate it. Multiply (-8x-3) by (ax-2): We get -8x^2 + 16x - 3ax + 6.

Then:

24x^2 + 25x - 47 = -8x^2 + 16x - 3ax + 6 - 53

Combining like terms: 32x^2 + 9x + 6 = -3ax + 6, or 32x^2 + 9x = -3ax

Since this derived equation is true for all values of x other than 2/a, arbitrarily choose x=1. Then:

32(1)^2 + 9(1) = -3a(1), or 32 + 9 = -3a, or 41 = -3a. Then a = -41/3

Unfortunately, this does not match any of the four answer choices. Another approach would be to substitute {-16, -3, 3, 16} for a in the given equation and determine whether or not the equation is true for each of these four values.

Answer 2

Multiply both sides by ax-2 and you should get 24x2+25x−47=(−8x−3)(ax−2)−53.
Multiply (-8x-3) and (ax-2) using FOIL (Firsts, Outsides, Insides, Lasts)
This gets you 24x2+25x−47=−8ax2−3ax+16x+6−53
You gotta reduce on the right side of the equation. 24x2+25x−47=−8ax2−3ax+16x−47
Since the coefficients of the x2-term are needed to be equal on both sides of the equation, −8a=24, or a=−3
The answer is -3