Question

select all the correct answers for which values is this expression underfunded x-1/x^2-2x-3 + 5/2x^2+2x

Answer 1

Undefined values for x

x = - 1 first

x= 3 third

x = 0 4th

Explanation:

An function f(x) is of the form g(x)/h(x) is undefined when the denominator h(x) becomes 0 since division by 0 is undefined

The denominators of the two individual expression can be factored as follows:

`x^2 - 2x - 3 = (x - 3)(x + 1)\\\\2x^2 + 2x = 2x(x + 1)\\\\`

2x² + 2x = 2x(x + 1)

The LCM of these two expressions is

`(x-3)(x+1)2x`

Therefore the expression

`(\left(x-1\right))/(x^2-2x-3)+(5)/(2x^2+2x)`

becomes

`=((x-1)(2x) + 5(x-3))/(2x(x-3)(x+1))}`

Looking at the denominator we see that the denominator becomes 0 when any of the individual terms becomes zero

Therefore when
2x = 0 ==> x = 0
(x - 3) = 0 ==> x = 3

(x+1) = 0 ==> x = - 1