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.