SOLUTION: Hi, Can someone assist me ont the following problem? x-6/x-7=1/x-7

Question 125878: Hi, Can someone assist me ont the following problem?
x-6/x-7=1/x-7
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression

Cross multiply

Foil

Subtract x from both sides. Add 7 to both sides.

Combine like terms

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for x in each case

Since we have a repeating answer, our only possible answer is

However, notice what happens when we plug in into the original equation

Start with the original equation

Plug in

Subtract. Since division by zero is undefined, is not a solution.

-------------------------------

Answer:

So there are no solutions.
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