Answer:
Option B is correct
Explanation:
Value of a is -3
Given the equation: [tex]\frac{24x^2+25x-47}{ax-2} =-8x-3-\frac{53}{ax-2}[/tex] is true for all [tex]x\neq 2a[/tex]
To find the value of a.
Multiply both sides of the given equation by [tex](ax-2)[/tex], we have;
[tex]24x^2+25x-47=(-8x-3)(ax-2)-53[/tex]
Using FOIL Method to multiply two binomials i.e (-8x-3)(ax-2)
[tex]24x^2+25x-47=-8ax^2+16x-3ax+6-53[/tex]
or
[tex]24x^2+25x-47=-8ax^2+x(16-3a)-47[/tex]
Since the coefficients of the [tex]x^2[/tex] term have to be equal on both sides of the equation. we have;
-8a = 24
Divide both sides by -8 we get;
a = -3
Therefore, the value of a is, -3
