9514 1404 393
Answer:
x = 4 or x = 5
Step-by-step explanation:
Maybe you want to solve ...
[tex]\dfrac{x-2}{x+2}-\dfrac{3}{x-2}=2\dfrac{x-11}{x^2-4}\\\\\dfrac{(x-2)^2-3(x+2)-2(x-11)}{x^2-4}=0\\\\\dfrac{x^2 -4x+4-3x-6-2x+22}{x^2-4}=0=\dfrac{x^2-9x+20}{x^2-4}\\\\{x^2-9x+20}=0=(x-5)(x-4)\ \Rightarrow\ x=\{4,5\}[/tex]
The solutions are x=4 and x=5.
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Additional comment
The Order of Operations requires that we interpret your input as ...
x -(2/x) +2 -(3/x) -2 = (2(x -11)/x^2) -4
This is probably not what you want.
In order to get the interpretation we have used above, you need to use parentheses around any numerator or denominator containing arithmetic operations:
(x -2)/(x +2) -3/(x -2) = 2(x -11)/(x^2 -4)
