The given equation x-1/x-2+x+3/x-4=2/(x-2).(4-x) is correct. the answer is proved.
According to the statement
we have given that the equation and we have to prove that the given answer is a correct answer for those equivalent equation.
So, The given expression are:
[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4} = \frac{2}{(x-2).(4-x)}[/tex]
And we have to prove the answer.
So, For this
[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4}[/tex]
[tex]\frac{({x-1}) ({x-4}) +({x+3})({x-2})} {(x-2) (x-4)}[/tex]
Then the equation become
[tex]\frac{x^{2} -4x -x +4 + x^{2} -2x + 3x -6 }{(x-2) (x-4)}[/tex]
Now solve it then
[tex]2x^{2} - 4x -2 / (x-2) (x-4)[/tex]
Now take 2 common from answer then equation become
[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4} = \frac{2}{(x-2).(4-x)}[/tex]
Hence proved.
So, The given equation x-1/x-2+x+3/x-4=2/(x-2).(4-x) is correct. the answer is proved.
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