SOLUTION: solve & check the equation, beginning algebra 6th edition chpt 5.5. i have no clue as to where to start on this problem. i am completely stuck on this problem, any help with this p

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Question 73765: solve & check the equation, beginning algebra 6th edition chpt 5.5. i have no clue as to where to start on this problem. i am completely stuck on this problem, any help with this problem will be appreciated.
5 / x + 2 + 2 / x ^ 2 + 7 x + 6 = 3 / x + 1

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

To get rid of the fractions, multiply everything by the LCD (the LCD is x^2)
Distribute the x^2
Combine like terms
Get everything to one side
Group the highlighted terms
Factor out a 7x^2 out of the 1st group of parenthesis and factor out a 2 out of the 2nd group of parenthesis. Notice how we have a common term of (x+1). We can combine them now
Combine the terms. If we let y=(x+1) it would look like Now we can solve for x.
Isolate each factor and solve:

There's our answer

This answer will not be real (I don't know if you know about complex roots yet), so I would ignore this factor.
So our answer is x=-1

Check
Plug in x=-1

Works