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avatar+580 

Find x+1/x if

 \[3x+\frac{2}{x}-4=2(x+9)-\left(7-\frac{1}{x}\right).\]

 Sep 9, 2022
 #1
avatar+357 
+1

3x+2/x-4=2x+18-7+1/x

3x+2/x-4=2x+1/x+11

3x+2/x+7=2x+1/x

3x+1/x+7=2x

[(3x+1/x+8)/2]/(3x+1/x+7)/2

 

This simplifies down to 

(3x^2+8x+1)/(3x^2+7x+1)

 

Yay!

 Sep 9, 2022
 #2
avatar+2444 
0

I don't think it was meant to be this complicated...

BuilderBoi  Sep 9, 2022
edited by BuilderBoi  Sep 9, 2022
 #3
avatar+2444 
0

\(3x+\frac{2}{x}-4=2(x+9)-(7-\frac{1}{x})\)

\(3x+\frac{2}{x}-4=2x + 18-7+\frac{1}{x}\)

\(3x + {1 \over x} - 4 = 2x + 11\)

\(x + {1 \over x} - 4 = 11\)

\(x + {1 \over x} = \color{brown}\boxed{15}\)

.
 Sep 9, 2022

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