Answer:
Value of the rational expression is 0 at x = 3.
Step-by-step explanation:
The given rational expression is [tex]\frac{x^{2}-2x-3 }{4x^{2} -12}[/tex]
We will factorize the numerator first.
x²-2x-3 = x²-3x+x-3
= x(x-3)+1(x-3)
= (x-3)(x+1)
Now we factorize denominator
4x²-12 = 4(x²-3)
Now the expression can be written as [tex]\frac{(x-3)(x+3)}{4(x^{2}-3) }[/tex]
At x = 3 the value of expression will be 0 because at x = 3 factor (x-3) becomes 0.
So the answer is at x = 3 rational expression
[tex]\frac{x^{2}-2x-3 }{4x^{2} -12}=0[/tex]
