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Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 2 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator of the previous fraction by 1. He then multiplies all his fractions together. He has 3 fractions, and their product equals 10. What is the value of the first fraction he wrote?

 May 28, 2024
 #1
avatar+129487 
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(x + 1 ) / (x - 1)  *   ( x + 2) / (x )  * ( x + 3) /( x +1)  = 10    simplify

 

(x + 2) (x + 3)  = 10 (x)(x -1)

 

x^2+ 5x + 6 = 10x^2 -10x

 

9x^2 - 15x - 6 =  0

                                                   

3x^2 - 5x - 2  = 0

 

(3x +1) (x -2)  = 0 

 

x =  2

 

The first fraction is    3 / 1

 

cool cool cool

 May 28, 2024

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