Question

What is the value of the rational expression x2--2x-3/4x2-12 when x=3

Answer 1

Value of the rational expression is 0 at x = 3.

Explanation:

The given rational expression is
`(x^(2)-2x-3 )/(4x^(2) -12)`

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
`((x-3)(x+3))/(4(x^(2)-3) )`

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

`(x^(2)-2x-3 )/(4x^(2) -12)=0`