Question

How do you simplify the fractional expressions `1/(x-3) - 1/(x+3) - 1/(x-1) +1/(x+1)`?

Answer 1

we just take L.C.M and use the formula
(a+b) (a-b)=(a²-b²)
after that the brackets are opened and it is simplified by cancelling like terms with opposite signs.

`((x²-1)(x+3)-(x²-1)(x-3)-(x²-9)(x+1)+(x²-9)(x-1))/((x²-1)(x²-9))`

`((x³+3x²-x-3)-(x³-3x²-x+3)-(x³+x²-9x-9)+(x³-x²-9x+9))/((x²-1)(x²-9)`

`(x³+3x²-x-3-x³+3x²+x-3-x³-x²+9x+9+x³+x²-9x+9)/((x²-1)(x²-9)`

`(4x²+9)/((x²-1)(x²-9)`