SOLUTION: 1. X - 2/4X = 1/6 2. 3/X + 5 = 3/3X - 2

Algebra ->  Rational-functions -> SOLUTION: 1. X - 2/4X = 1/6 2. 3/X + 5 = 3/3X - 2      Log On


   

Question 118005This question is from textbook
: 1. X - 2/4X = 1/6

2. 3/X + 5 = 3/3X - 2 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1

%28x-2%29%2F%284x%29=%281%29%2F%286%29 Start with the given equation


Multiply both sides by the LCD %284x%29%286%29. Doing this will eliminate every fraction.


%286%29%28x-2%29=%281%29%284x%29 Distribute and multiply. Notice every denominator has been canceled out.




6x-12=4x Distribute again


6x=4x%2B12Add 12 to both sides


6x-4x=%2B12 Subtract 4x from both sides


2x=12 Combine like terms on the left side


x=%2812%29%2F%282%29 Divide both sides by 2 to isolate x



x=6 Divide

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Answer:
So our answer is x=6







#2



%283%29%2F%28x%2B5%29=%283%29%2F%283x-2%29 Start with the given equation


Multiply both sides by the LCD %28x%2B5%29%283x-2%29. Doing this will eliminate every fraction.


%283x-2%29%283%29=%28x%2B5%29%283%29 Distribute and multiply. Notice every denominator has been canceled out.


9x-6=3x%2B15 Distribute again



9x=3x%2B15%2B6Add 6 to both sides


9x-3x=15%2B6 Subtract 3x from both sides


6x=15%2B6 Combine like terms on the left side


6x=21 Combine like terms on the right side


x=%2821%29%2F%286%29 Divide both sides by 6 to isolate x



x=7%2F2 Reduce

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Answer:
So our answer is x=7%2F2 (which is approximately x=3.5 in decimal form)