a for aargh!

Algebra Level 2

24 x 2 + 25 x − 47 a x − 2 = − 8 x − 3 − 53 a x − 2 \large \frac{24x^2+25x-47}{ax-2}=-8x-3-\frac{53}{ax-2}

The equation above is true for all values of x ≠ a x\neq{a} , where a a is a constant. What is the value of a a ?


The answer is -3.

Terry Yu by Terry Yu , 17, USA

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1 solution

Terry Yu
May 15, 2017

  1. Multiply both sides by a x − 2 ax-2 , getting 24 x 2 + 25 x − 47 = ( − 8 x − 3 ) ( a x − 2 ) − 53 24x^2+25x-47=(-8x-3)(ax-2)-53

  2. Simplify, getting 24 x 2 + 25 x − 47 = − 8 a x 2 − 3 a x + 16 x + 6 − 53 24x^2+25x-47=-8ax^2-3ax+16x+6-53

  3. Simplify, getting 24 x 2 + 25 x − 47 = − 8 a x 2 − 3 a x + 16 x − 47 24x^2+25x-47=-8ax^2-3ax+16x-47

Since the coefficients of the x 2 x^2 -term have to be equal on both sides of the equation, − 8 a = 24 -8a=24 , and a = − 3 a=\large\color{#D61F06}\boxed{-3} .

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