Question

Solve :
$\underset{x\to a}{lim}(x-a)(\frac{1}{x-a}-\frac{1}{x^2-(a+b)x+ab})=$ __________.

• A. $\frac{a-b-c}{a-b}$
• B. $o$
• C. $1$
• D. $\frac{a+b}{a-b}$

Answer 1

Answer: (A)

$\frac{a-b-c}{a-b}$

$\begin{array}{c}{lim}_{x\to a}\left(x-a\right)\left(\frac{1}{x-a}-\frac{1}{x^2-\left(a+b\right)x+ab}\right)\\ ={lim}_{x\to a}\left(x-a\right)\left(\frac{1}{x-a}-\frac{1}{\left(x-a\right)\left(x-b\right)}\right)\\ ={lim}_{x\to a}\left(x-a\right)\left(\frac{x-b-1}{\left(x-a\right)\left(x-b\right)}\right)\\ =\frac{a-b-1}{a-b}\end{array}$