SOLUTION: Hello, I am asked in this set of homework problems to perform the indicated operations and simplify: 1- 2x-1/x^2-4 over (or divided by) 1+ 1/x-2 Translation: 1- (is out f

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Question 92045: Hello,
I am asked in this set of homework problems to perform the indicated operations and simplify:
1- 2x-1/x^2-4 over (or divided by) 1+ 1/x-2
Translation:
1- (is out front of the equation) then 2x-1 is divided by x^2-4 then a larger division sign 1+ (is out front of the equation) then 1 divided by x-2
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
1- 2x-1/x^2-4 over (or divided by) 1+ 1/x-2
[1 -(2x-1)/(x^2-4)] / [1 + 1/(x-2)]
[[(x^2-4)-(2x-1)]/(x^2-4)] / [x-2+1]/(x-2)
= [[x^2-2x-3]/(x^2-4)] / [(x-1)/(x-2)]
Invert the denominator and multiply as follows:
= [(x-3)(x+1)/(x-2)(x+2)] * [(x-2)/(x-1)]
Cancel where you can to get:
= [(x-3)(x+1)]/[(x+2)(x-1)]
Cheers,
Stan H.