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Question

# Find each limit. $\lim _{x \rightarrow 3}\left(\frac{x^{2}}{x-3}-\frac{3 x}{x-3}\right)$

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We would like to find the limit for the following expression.

$\color{#4257b2}\lim\limits_{x\to3}\ \left(\dfrac{x^2}{x-3}-\dfrac{3x}{x-3}\right)$

$\lozenge$\ \ $\text{\underline{\bf{Solution:}}}$

Simplify the expression as follows:

$\lim\limits_{x\to3}\ \left(\dfrac{x^2}{x-3}-\dfrac{3x}{x-3}\right)=\lim\limits_{x\to3}\ \left(\dfrac{x^2-3x}{x-3}\right)$

Use GCF property as follows:

$\lim\limits_{x\to3}\ \left(\dfrac{x(x-3)}{x-3}\right)$

$\lim\limits_{x\to3}\ (x)$

According the rule of the limit property as follows:

$\because\ \ \lim\limits_{x\to a}\ (x)=a$

$\therefore\ \ \lim\limits_{x\to3}\ (x)=3$

$\color{#c34632}\lim\limits_{x\to3}\ \left(\dfrac{x^2}{x-3}-\dfrac{3x}{x-3}\right)=3$

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