Question

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______________
The equation
24x2+25x−47
ax−2
=−8x−3−
53
ax−2
is true for all values of x≠
2
a
, where a is a constant.

What is the value of a?​

Answer 1

Answer:

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it is true that (−8x − 3)(ax − 2) − 53 = 24x2 +25x −47. (This can be seen by multiplying each side of the given equation by ax − 2). This can be rewritten as −8ax2+ 16x − 3ax = 24x2+ 25x − 47.

Answer 2

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

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

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

$\bold{ \longrightarrow24x^{2} + 25x - 47 = ( - 8x - 3)(ax - 2) - 53}$

$\bold{ \longrightarrow24x^{2} + 25x - 47 = - 8ax ^{2} + 16x - 3ax + 6 - 53 }$

$\bold{ \longrightarrow24x^{2} + 25x - 47 = - 8ax ^{2} + 16x - 3ax - 47}$

$\bold{ \longrightarrow24x^{2} + 25x = - 8ax ^{2} + (16x - 3)}$

$\bold{24 = - 8a}$

$\bold \green{a = - 3}$

$\mathfrak{hence \: this \: is \: the \: required \: answer}$