SOLUTION: solve and check each of the following equations for x. 5/x+6+2/x^2+7x+6=3/x+1

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Question 116168: solve and check each of the following equations for x. 5/x+6+2/x^2+7x+6=3/x+1
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
5%2F%28x%2B6%29%2B2%2F%28x%5E2%2B7x%2B6%29=3%2F%28x%2B1%29 Start with the given expression


5%2F%28x%2B6%29%2B2%2F%28%28x%2B1%29%28x%2B6%29%29=3%2F%28x%2B1%29 Factor


%28%28x%2B6%29%28x%2B1%29%29%285%2F%28x%2B6%29%2B2%2F%28%28x%2B1%29%28x%2B6%29%29%29=%28%28x%2B6%29%28x%2B1%29%29%283%2F%28x%2B1%29%29 Multiply both sides by the LCD %28x%2B6%29%28x%2B1%29



5%28x%2B1%29%2B2=3%28x%2B6%29 Distribute


5x%2B5%2B2=3x%2B18 Distribute again


5x%2B7=3x%2B18 Combine like terms on the left side


5x=3x%2B18-7Subtract 7 from both sides


5x-3x=18-7 Subtract 3x from both sides


2x=18-7 Combine like terms on the left side


2x=11 Combine like terms on the right side


x=%2811%29%2F%282%29 Divide both sides by 2 to isolate x


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Answer:
So our answer is x=11%2F2 (which is approximately x=5.5 in decimal form)