perform the indicated operation and give the answer in simplified form.
((x-1/x+1)-(x+1)/(x-1))/
((x-1/x+1)-(x+1)/(x-1))
=0 ?
since the numerator and denominator are equal, the answer is 1
oh okay, thanks.
To simplify the expression and find the answer, we need to perform the indicated operations step by step.
First, let's simplify the numerator of the expression:
((x - 1)/(x + 1)) - ((x + 1)/(x - 1))
To find the least common denominator (LCD) of the two fractions, we need to factor the denominators:
x + 1 and x - 1
(x + 1)(x - 1)
Since the denominators have common factors, we can rewrite and combine the terms:
((x - 1)(x - 1) - (x + 1)(x + 1)) / ((x + 1)(x - 1))
Expanding the numerator:
(x^2 - 2x + 1 - (x^2 + 2x + 1)) / ((x + 1)(x - 1))
Adding like terms in the numerator:
(x^2 - 2x + 1 - x^2 - 2x - 1) / ((x + 1)(x - 1))
Simplifying the numerator:
(-4x) / ((x + 1)(x - 1))
Now, let's focus on the denominator of the expression:
((x - 1)/(x + 1)) - ((x + 1)/(x - 1))
The denominator is the same as the numerator, so we have (-4x) / ((x + 1)(x - 1)) as the numerator and ((x + 1)(x - 1)) as the denominator.
To simplify the expression further, we notice that the numerator and denominator are equivalent. Therefore, any value of x will make this expression equal to 1, not 0.
So, the answer is not 0, but rather 1.