Answer:
B. -3
Explanation:
Our equation is: [tex]\frac{24x^2+25x-47}{ax-2} =-8x-3-\frac{53}{ax-2}[/tex] . We see that both sides have a term with denominator ax - 2, so let's add [tex]\frac{53}{ax-2}[/tex] to both sides:
[tex]\frac{24x^2+25x-47}{ax-2} =-8x-3-\frac{53}{ax-2}[/tex]
[tex]\frac{24x^2+25x-47}{ax-2}+\frac{53}{ax-2} =-8x-3[/tex]
[tex]\frac{24x^2+25x+6}{ax-2}=-8x-3[/tex]
Now multiply both sides by ax - 2:
[tex]24x^2+25x+6=(-8x-3)(ax-2)=-8ax^2-3ax+16x+6[/tex]
[tex]24x^2+25x+6=(-8a)x^2+(16-3a)x+6[/tex]
We essentially want to make the terms on each side match. Look at the coefficient of x² on the left side: it's 24. That means on the right side, it should be 24, as well. Then, set -8a equal to 24:
-8a = 24
a = -3
Thus, the answer is B.
