how to simplify (x^3-x)/(x-1)

x³-x

=x(x²-1)
=x(x+1)(x-1)
Can you take it from here?

thanks!

You're welcome!

To simplify the expression (x^3 - x)/(x - 1), you can perform polynomial long division. Here's how you can do it step by step:

Step 1: Write the dividend (x^3 - x) and the divisor (x - 1) in the long division format:

_________________________
x - 1 | x^3 - x

Step 2: Divide the first term of the dividend (x^3) by the first term of the divisor (x):

_______________________
x - 1 | x^3 - x
- (x^3 - x)
____________
0

Step 3: Multiply the divisor (x - 1) by the quotient from the previous step (0):

_______________________
x - 1 | x^3 - x
(0)
____________
0

Step 4: Subtract the result of the previous multiplication from the dividend:

_______________________
x - 1 | x^3 - x
- (0)
____________
x^3 - x

Step 5: Bring down the next term of the dividend (-x):

_______________________
x - 1 | x^3 - x
- (0)
____________
x^3 - x
- (-x)

Step 6: Divide the new dividend (x^3 - x) by the first term of the divisor (x):

_______________________
x - 1 | x^3 - x
- (0)
____________
x^3 - x
- (-x)
___________
x

Step 7: Multiply the divisor (x - 1) by the new quotient (x):

_______________________
x - 1 | x^3 - x
(0)
____________
x^3 - x
- (-x)
___________
x

Step 8: Subtract the result of the previous multiplication from the new dividend:

_______________________
x - 1 | x^3 - x
- (0)
____________
x^3 - x
- (-x)
___________
x + x

Step 9: Simplify the expression that remains (x + x) to get 2x.

Therefore, the simplified form of (x^3 - x)/(x - 1) is x + 2.

Note: You can also verify the result by factoring the original expression, but polynomial long division allows for a step-by-step simplification process.