simplify: $\frac{2x - 1}{x^{2}-1}+\frac{1}{x - 1}$\na. $\frac{3x - 1}{x + 1}$\nb. $\frac{3x}{(x + 1)(x…

Explanation:

Step1: Factor the denominator

Since (x^{2}-1=(x + 1)(x - 1)), the expression becomes (\frac{2x-1}{(x + 1)(x - 1)}+\frac{1}{x - 1}).

Step2: Find a common - denominator

The common denominator of ((x + 1)(x - 1)) and ((x - 1)) is ((x + 1)(x - 1)). Rewrite (\frac{1}{x - 1}) as (\frac{x + 1}{(x + 1)(x - 1)}).

Step3: Add the fractions

(\frac{2x-1}{(x + 1)(x - 1)}+\frac{x + 1}{(x + 1)(x - 1)}=\frac{2x-1+x + 1}{(x + 1)(x - 1)}).

Step4: Simplify the numerator

Combine like - terms in the numerator: (2x-1+x + 1=3x). So the fraction is (\frac{3x}{(x + 1)(x - 1)}).

Answer:

B. (\frac{3x}{(x + 1)(x - 1)})