SOLUTION: I ned help. I have been having problem solving these questions. Kindly help me on these 2 questions. 1: Find all of the errors in the following solution to an equation. 7/

Question 99088: I ned help. I have been having problem solving these questions. Kindly help me on these 2 questions.
1: Find all of the errors in the following solution to an equation.
7/x = 8/x+3 +1
7(x+3) = 8x + 1
7x + 3 = 8x + 1
-x = -3
x = 3
2: What are extraneous solutions of an equation? Why do they sometimes occur in the process of solving rational or radical equations?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1: Find all of the errors in the following solution to an equation.
7/x = 8/x+3 +1
7(x+3) = 8x + 1
7x + 3 = 8x + 1
-x = -3
x = 3
---------------
Comment: I'll do it the right way and let you identify the requested errors.
-------------------
7/x = 8/(x+3) +1
Multiply thru by x(x+3) to get:
7(x+3) = 8(x) + x(x+3)
----------------
7(x+3) = 8x + 1
7x+21 = 8x+1
---------------------
7x + 3 = 8x + 1
-x = -2
----------------------
2: What are extraneous solutions of an equation? Why do they sometimes occur in the process of solving rational or radical equations?
---------
Extraneous solutions arrise when solving an equation requires
raising both sides of the equation to a higher power.
For example:
If you start with
x = 1, the answer is obviously x=1
But if you square both sides you get:
x^2=1
Then x^2 - 1 = 0
Then (x+1)(x-1) = 0
Then x=-1 or x=1
You now have two "solutions".
But if you try these two "solutions" in the original equation
you find that x=-1 is extraneous.
============
Cheers,
Stan H.
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