If 2x - 1overx = 7, x ≠ 0, then what is the value of 8x⁶+5x³-1over8x⁶-25x³-1 ?

If 2x - 1overx = 7, x ≠ 0, then what is the value of…

If 2x - $1\over{x}$ = 7, x ≠ 0, then what is the value of $8x^6+5x^3-1\over{8x^6-25x^3-1}$ ?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. $13\over12$ .

2x - 1/x = 7

⇒ (2x - 1/x)³ = 7³ = 343

⇒ 8x³ - 1/x³ - 3(2x)(1/x)(2x - 1/x) = 343

⇒ 8x³ - 1/x³ - 42 = 343

⇒ 8x³ - 1/x³ = 385

⇒ 8x⁶ - 1 = 385x³

$8x^6+5x^3-1\over{8x^6-25x^3-1}$ = (385x³ + 5x³)/(385x³ - 25x³) = 390/360 = 13/12