Question

Can you help me with this please..

Answer 1

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.