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Answer 1

$Given : \frac{24x^2 + 25x - 47}{ax - 2} = -8x - 3 - \frac{53}{ax - 2}$

LCM on both sides = ax - 2.


$\frac{24x^2 + 25x - 47}{ax - 2} = \frac{-8x(ax - 2) - 3(ax - 2) - 53}{ax - 2}$


On canceling ax - 2 from both sides, The equation looks like,

24x^2 + 25x - 47 = -8x(ax - 2) - 3(ax - 2) - 53

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

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

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

24x^2 + 9x + 3ax = -8ax^2

24x^2 + 8ax^2 + 9x + 3ax = 0

x^2(24 + 8a) + x(9 + 3a) = 0

x^2(8(a + 3)) + x(3(a + 3)) = 0

8x^2(a + 3) + 3x(a + 3) = 0

(8x^2 + 3x)(a + 3) = 0

x(8x + 3)(a + 3) = 0

x = 0 (or) x = 8x + 3 = 0 (or) a + 3 = 0

x = 0, x = -3/8 , a = -3.


Hope this helps!

Answer 2

Hi,

Please see the attached file!


I hope my answer and my steps are correct.


Thanks