how to simplify ((x^3)-x)/(x-1)
math help needed.
pull out the x in the numerator:
x(x^2-1)/(x-1)
[x(x+1)(x-1)]/(x-1)
now can you reduce it further?
To simplify the expression ((x^3)-x)/(x-1), you can use polynomial division or factoring. Here's how you can do it using factoring:
Step 1: Factor the numerator, ((x^3)-x).
We can factor out x from each term:
x(x^2-1)
Step 2: Factor the difference of squares in the numerator.
The term (x^2-1) is a difference of squares and can be factored as (x+1)(x-1).
Step 3: Simplify the expression.
Now, the expression becomes (x(x+1)(x-1))/(x-1).
Step 4: Cancel out the common factor.
We can cancel out the common factor (x-1) from both the numerator and the denominator.
The final simplified expression is x(x+1).
Therefore, ((x^3)-x)/(x-1) simplifies to x(x+1).