Please divide the following polynomial

(X^2 -4)/(x-1)

please help me solve this... asap! Thank you :)

x^2-4=(x+2)(x-2) which has no factor (x-1) hence there is not much point in dividing because result will not be without remainder:
x + (x-4)/(x-1)=

x+1 + (-3)/(x-1)=

x+1 + 3/(1-x)

(X^2 -4)/(x-1) = (x + 2)(x - 2)/(x - 1), which obviously does not divide evenly

(X^2 -4)/(x-1) = x + 1 with remainder 5

..........x + 1 + -3/(x -1)
......._______________
x - 1| x² + 0x - 4
.........-x² +1x....................x(x - 1) = x² - x now subtract from P(x)
........-----------
................1x - 4..............Bring down next term.
................-1x + 1.............1(x - 1) now subtract from P(x)
.................----------
.......................-3... this is our remainder write it as a fration over the divisor.

x - 1) x^2 - 4( x + 1
x^2 - x
---------
x - 4
x - 1
--------
-3
---------

Answer: (x + 1) remainder -3