we first consider x-5/x - (-12/x-1), then
x-5/x - (-12/x-1) = x-5/x + 12/x-1
Taking L.C.M x(x-1), we get
[(x-5)(x-1) + x(12)] / x(x-1)
(x^2 - 6x + 5 +12x)/x(x-1)
HENCE (x^2 + 6x + 5 )/x(x-1)
Now consider x+1/x + x+1/x-1
[(x+1)(x-1) + x(x+1)] / x(x-1)
(x^2 -1 + x^2 +x) / x(x-1)
(2x^2 +x -1) / x(x-1)
HENCE (2x^2 +x -1) / x(x-1)
Now when we put the values x(x-1) will cancel out each other, then we get
(x^2 + 6x + 5 ) / (2x^2 +x -1)
By simplifying above equations, we get
(x+1)(x+5) / (2x-1)(x+1)
Now (x+1) will cancel out each other, then
HENCE (x+5) / (2x-1)
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