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Help me!

 

Let
f(x) = \frac{4x - 1}{5x + 2} + \frac{2x + 3}{x}
For what value of a is f(a) = 3?

 Dec 21, 2023
 #1
avatar+126665 
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\( \frac{4x - 1}{5x + 2} + \frac{2x + 3}{x} \)

 

3 = (4x -1) / (5x + 2)  +  (2x + 3) / x

 

3=   [(4x -1)(x) ]  + (5x + 2)(2x + 3) ]  /  [ (5x + 2) (x) ]

 

3 [ (5x +2) x ]=   14x^2 + 18x + 6

 

15x^2 +6x  =  14x^2 + 18x + 6

 

x^2 - 12x - 6  =  0

 

x^2 - 12x  + 36 =  6 + 36

 

(x - 6)^2  = 42

 

x - 6 =    ± sqrt (42)

 

x = 6 ± sqrt (42)

 

 

cool cool cool

 Dec 21, 2023

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