Question 114260: Hello out there,I need some help with some problems,the first one is,Solve 6/x+2=2/x-4.The next one is,Solve 3/x+4-1/x=1/x.The third one is,Solve x/5=x+4/9.And the last one is,Solve 1/2x+1/x=3/8,thanks to whoever can help.
Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Ok, I'll do one, and then let you work on the rest.
This one is interesting because there are two ways to approach the solution. One of them is very simple and leads directly to the answer, and the other is rather more complex but illustrates a more general method of solution that you can use in many more situations. I'll show you both.
First the complex way:
Step 1: Notice that if x = 0 or x = -4, you will have a zero in the denominator, so remember to check the ultimate answer against these two values to ensure that you have a valid solution.
Step 2: Find a common denominator for the left side of the equation. The best we can do is  , so
Step 3: Then combine terms, cross-multiply, and solve:
 , Divide both sides by x,
 , then add 4 to both sides
 , then subtract x from both sides
 .
Note that this answer is not one of the excluded values, so it is valid.
Now for the simple way,
Step 1: Same as step 1 above.
Step 2: Add  to both sides
Step 3: Cross multiply and solve:
.
We got the same answer, so that is a very good sign. But we still need to check the answer in the original equation:
 , Check.
Ok, your turn. Apply what you have learned to the other three problems.
Hope this helps,
John
Answer by MathLover1(20849)  (Show Source):
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