Given:
The equation is,
[tex]\frac{24x^2+25x-47}{ax-2}=-8x-3-\frac{53}{ax-2}[/tex]
Explanation:
Simplify the right hand side of equation.
[tex]\begin{gathered} -8x-3-\frac{53}{ax-2}=\frac{(-8x-3)(ax-2)-53}{ax-2} \\ =\frac{-8ax^2-3ax+16x+6-53}{ax-2} \\ =\frac{-8ax^2+(-3a+16)x-47}{ax-2} \end{gathered}[/tex]
From left side and right side of equationn it can be observed that,
[tex]-8ax^2=24x^2\text{ and (-3a+16)x=}25x[/tex]
Simplify the equation for a.
[tex]\begin{gathered} -8a=24 \\ a=\frac{24}{-8} \\ =-3 \end{gathered}[/tex]
OR,
[tex]\begin{gathered} -3a+16=25 \\ -3a=25-16 \\ a=\frac{9}{-3} \\ =-3 \end{gathered}[/tex]
So value of a is -3.
Option B is correct.
