Answer:
The restrictions on the variable x in the expression [tex]\frac{x^2+3x+2}{x^2-4x-12}[/tex] is [tex]x\neq6[/tex]
Step-by-step explanation:
Given : Expression [tex]\frac{x^2+3x+2}{x^2-4x-12}[/tex]
To find : Identify the restrictions on the variable ?
Solution :
First we simplify the expression,
[tex]\frac{x^2+3x+2}{x^2-4x-12}[/tex]
Applying middle term split to factor,
[tex]=\frac{x^2+2x+x+2}{x^2-6x+2x-12}[/tex]
[tex]=\frac{x(x+2)+1(x+2)}{x(x-6)+2(x-6)}[/tex]
[tex]=\frac{(x+2)(x+1)}{(x-6)(x+2)}[/tex]
Cancel the like term in Nr. and Dr.,
[tex]=\frac{x+1}{x-6}[/tex]
Now, To find restriction for x set each polynomial or term in the denominator to cannot equal to 0.
So, Put denominator = 0
[tex]x-6=0[/tex]
[tex]x=6[/tex]
Which means the restriction is [tex]x\neq6[/tex]
Therefore, The restrictions on the variable x in the expression [tex]\frac{x^2+3x+2}{x^2-4x-12}[/tex] is [tex]x\neq6[/tex]
