Question

What is the domain of the rational expression ? thanks :))


`\frac{3x}{x { }^( 2 ) - 8x + 16}`

Answer 1

Domain is defined as the values of input for which output is defined.

In a rational expression we must not have denominator as 0

so let us equate denominator=0 and find the restriction on domain by finding x

x²-8x+16=0

x²-8x+4²=0

(x-4)²=0

x=4

so domain is all real numbers except x=4

Answer 2

In a rational expression , the denominator should not be zero. SO we need to find those values for x which makes the denominator 0 . And we need to exclude those values from the domain .

`x^2 -8x+16=0 => (x-4)^2=0=>x=4`

So when x =4, denominator becomes zero, so x=4 is not a part of the domain . Therefore the required domain is

`(- \infty,4)U(4,\infty)`