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(1+x)/(2-x)
Limit of the function/ (1+x)/(2-x)

Limit of the function (1+x)/(2-x)

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     /1 + x\
 lim |-----|
x->2+\2 - x/
$$\lim_{x \to 2^+}\left(\frac{x + 1}{2 - x}\right)$$ 
Limit((1 + x)/(2 - x), x, 2)
Detail solution
Let's take the limit
$$\lim_{x \to 2^+}\left(\frac{x + 1}{2 - x}\right)$$
transform
$$\lim_{x \to 2^+}\left(\frac{x + 1}{2 - x}\right)$$
=
$$\lim_{x \to 2^+}\left(\frac{x + 1}{2 - x}\right)$$
=
$$\lim_{x \to 2^+}\left(- \frac{x + 1}{x - 2}\right) = $$
False

= -oo

The final answer:
$$\lim_{x \to 2^+}\left(\frac{x + 1}{2 - x}\right) = -\infty$$
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
Plot the graph
Rapid solution [src] 
-oo
$$-\infty$$
Expand and simplify
One‐sided limits [src] 
     /1 + x\
 lim |-----|
x->2+\2 - x/
$$\lim_{x \to 2^+}\left(\frac{x + 1}{2 - x}\right)$$ 
-oo
$$-\infty$$ 
= -454.0
     /1 + x\
 lim |-----|
x->2-\2 - x/
$$\lim_{x \to 2^-}\left(\frac{x + 1}{2 - x}\right)$$ 
oo
$$\infty$$ 
= 452.0
= 452.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 2^-}\left(\frac{x + 1}{2 - x}\right) = -\infty$$
More at x→2 from the left
$$\lim_{x \to 2^+}\left(\frac{x + 1}{2 - x}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{x + 1}{2 - x}\right) = -1$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x + 1}{2 - x}\right) = \frac{1}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x + 1}{2 - x}\right) = \frac{1}{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x + 1}{2 - x}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x + 1}{2 - x}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x + 1}{2 - x}\right) = -1$$
More at x→-oo
Numerical answer [src] 
-454.0
-454.0
The graph
Limit of the function (1+x)/(2-x)
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