in equation x - 1/x
________
x + 1/x My answer key said the answer was x squared -1
_____________
squared + 1
I'm wandering why it wouldn't simply be
x-1
______
x+1
i meant my answer was x squared - 1
______________
x squared +1
original equation x-1/x
________
x+1/x
equation? Where is the equal sign? I have no idea what you need to do.
As Bob noted you don't have an equation.
you probably have the expression
(x - 1/x)/(1 + 1/x)
and are asked to simplify it.
Hint: how about multiplying the fraction by x/x
yes the directions are to simplify
(x^2-1)
-------
(x+1)
(x+1)(x-1)
-----------
(x+1)
= x-1
To understand the solution, let's simplify the expression step by step.
First, let's simplify the numerator: x - 1/x.
To eliminate the fraction in the numerator, we need to find a common denominator. The common denominator for x and 1/x is x. So we can rewrite the numerator as (x^2 - 1)/x.
Next, let's simplify the denominator: x + 1/x.
Similarly, to eliminate the fraction in the denominator, we find a common denominator, which is also x. So we can rewrite the denominator as (x^2 + 1)/x.
Now we have the expression as (x^2 - 1)/x divided by (x^2 + 1)/x:
(x^2 - 1)/x ÷ (x^2 + 1)/x
When dividing fractions, we can multiply the numerator by the reciprocal of the denominator:
(x^2 - 1)/x * x/(x^2 + 1)
This simplifies to:
(x^2 - 1)/(x^2 + 1)
At this point, we have simplified the expression and it does not match the form mentioned in the answer key, which is x^2 - 1. It seems there might be an error in the answer key.
So, based on the calculations, the simplified expression is (x^2 - 1)/(x^2 + 1), not x^2 - 1.