Answer:
0.5
Step-by-step explanation:
Ok, so it's asking for what (1/(x-1) - 2/(x^2-1)) approaches as x approaches 1. Before we deal with the limit, let's simplify the inside.
We want to combine the two fractions into one fraction. Therefore, we need a common denominator.
1/(x-1) is equal to (x+1)/((x+1)(x-1) is equal to (x+1)/(x^2-1).
the inside expression is therefore (x+1)/(x^2-1) - 2/(x^2-1)
which simplifies to (x-1)/(x^2-1).
and that simplifies further to 1/(x+1).
Now this is a continuous function when x = 1, so to find the limit as x approaches 1 of this function, we can by definition just plug 1 in.
limx->1 (1/(x+1)) = 1/2.
The reason why we didn't just plug 1 in at the beginning is because the function wasn't continuous when x was 1.
