Simplify.
2x^3-2x
________
7x^3-14x^2+7x
= 2x(x^2 - 1)/( 7x(x^2 - 2x +1)
= 2x(x-1)(x+1)/(7x(x-1)(x-1))
= 2(x+1)/(7(x-1))
or
(2x+2x)/(7x - 7) , x ≠ 1
To simplify the given expression, we can factor out a common term from both the numerator and denominator.
Factoring out a common term can be done by looking for the greatest common factor (GCF) of the numerator and denominator. In this case, both terms have a common factor of 2x:
Numerator: 2x^3 - 2x = 2x(x^2 - 1)
Denominator: 7x^3 - 14x^2 + 7x = 7x(x^2 - 2x + 1)
Now, we can cancel out the common factor of 2x:
(2x(x^2 - 1)) / (7x(x^2 - 2x + 1))
Finally, we simplify further if possible. We notice that the expression (x^2 - 1) in the numerator and (x^2 - 2x + 1) in the denominator have a common factor of (x - 1). By factoring further, we get:
((x - 1)(x + 1)) / (7x(x - 1)(x - 1))
The (x - 1) in the numerator and denominator can be canceled out:
(x + 1) / (7x(x - 1))
So, the simplified form of the expression is (x + 1) / (7x(x - 1)).