SOLUTION: For the following, solve. Find exact solutions {{{3/(8x+1)+8/(2x+5)=1}}}

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Question 142983: For the following, solve. Find exact solutions

3%2F%288x%2B1%29%2B8%2F%282x%2B5%29=1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%2F%288x%2B1%29%2B8%2F%282x%2B5%29=1 Start with the given equation



%288x%2B1%29%282x%2B5%29%283%2Fcross%288x%2B1%29%2B8%2Fcross%282x%2B5%29%29=1 Multiply both sides by the LCD %288x%2B1%29%282x%2B5%29


3%282x%2B5%29%2B8%288x%2B1%29=%288x%2B1%29%282x%2B5%29 Distribute


6x%2B15%2B64x%2B8=%288x%2B1%29%282x%2B5%29 Distribute again


6x%2B15%2B64x%2B8=16x%5E2%2B42x%2B5 Foil


6x%2B15%2B64x%2B8-16x%5E2-42x-5=0 Subtract 16x^2 from both sides. Subtract 42x from both sides. Subtract 5 from both sides.


-16x%5E2%2B28x%2B18=0 Combine like terms



-2%284x-9%29%282x%2B1%29=0 Factor the left side



Now set each factor equal to zero:
4x-9=0 or 2x%2B1=0

x=9%2F4 or x=-1%2F2 Now solve for x in each case


So our answers are

x=9%2F4 or x=-1%2F2