Question

Evaluate
$\rm \displaystyle \lim_{n\to 2}\ \frac{x}{x-2}-\frac{4}{x^{2}-2x}$

Answer 1

Solution :

x/(x-2) - 4/(x²-2x)

= 1/(x-2) - 4/[x(x-2)]

= 1/(x-2)[ x- 4/x ]

= 1/(x-2)[ (x² - 2² )/x

= (x² - 2²)/[x(x-2)]

= [(x+2)(x-2)]/[x(x-2)]

After cancellation , we get

= ( x+2 )/x ----( 1 )

Now ,

$\rm \displaystyle \lim_{n\to 2}\ \frac{x}{x-2}-\frac{4}{x^{2}-2x}$
=$\rm \displatstyle \lim_{n\to 2}\ \frac{(x+2)}{x}$

= ( 2 + 2 )/2

= 4/2

= 2

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