Respuesta :

Answer: 4a. 1/2

See explanation

Step-by-step explanation:

4. a. Make a table of values ranging from 1 to 3.

(x^2-2x)/(x^2-4)=

[tex]\frac{x(x-2)}{(x-2)(x+2)}[/tex]=

[tex]\frac{x}{x+2}[/tex]=

2/(2+2)=

2/4=1/2

b.x->[tex]-2^{-}[/tex]: [tex]\frac{x}{x+2\\}[/tex]=

[tex]\frac{-2}{-2^-+2\\}[/tex]=

[tex]\frac{-2}{-0^-\\}[/tex]=∞

x->[tex]-2^{+}[/tex]: [tex]\frac{x}{x+2\\}[/tex]=

[tex]\frac{-2}{-2^++2\\}[/tex]=

[tex]\frac{-2}{0^+\\}[/tex]=-∞

c. When simplified, g(x)=[tex]\frac{x}{x+2}[/tex]. Hence, when you plug in x=2 to the equation, you get 2/(2+2) which equals 1/2. However, when you plug in x=-2 to the equation, you get -2/(-2+2) which is -2/0. -2/0 is undefined since the denominator can't be equaled to 0.

azikennamdi

The answer to expression A is 2/4=1/2. See the explanation below.

What is the explanation justifying the above?

Make a table of values ranging from 1 to 3.

(x^2-2x)/(x^2-4)= [x (x-2)]/ [(x-2) (x + 2)

= x/ [x +2]

= 2/(2+2)

2/4=1/2

Expression B

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

= -2/-0 = ∞

x->-2+: (x)/(x+2)

= (-2)/(-2+2)

= -2/0

= -∞

c. When simplified,

g(x)=. (x)/(x+2)

Hence, when you plug in x = 2 into the equation, you get 2/(2+2) which equals 1/2. However, when you plug in x=-2 to the equation, you get -2/(-2+2) which is -2/0. -2/0 is undefined since the denominator can't be equaled to 0.

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