Answer :
The value of the constant a in the given expression (24x² + 25x - 47)/(ax - 2) = −8x − 3 - 53/(ax - 2) is; a = -3
How to solve Algebraic Equations?
We are given the equation;
(24x² + 25x - 47)/(ax - 2) = −8x − 3 - 53/(ax - 2)
This can be simplified further as;
(24x² + 25x - 47)/(ax - 2) = [(−8x − 3)(ax - 2) - 53]/(ax - 2)
Now, multiply both sides by ax - 2 to get;
(24x² + 25x - 47)= [(−8x − 3)(ax - 2) - 53]
Multiply out the brackets to get;
24x² + 25x - 47 = -8ax² + 16x - 3ax + 6 - 53
24x² + 25x - 47 = -8ax² + 16x - 3ax - 47
24x² + 25x = -8ax² + 16x - 3ax
24x² + 25x = -8ax² + (16 - 3a)x
Thus;
16 - 3a = 25
3a = 16 - 25
a = -9/3
a = -3
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