Question

Could someone kindly help me in finding a solution?

Answer 1

see explanation

Explanation:

(a)

`(g)/(h)` =
`(g(x))/(h(x))` =
`(x+5)/((x-2)(x+2))`

Substitute x = - 1 into the expression

`(g)/(h)` (- 1 ) =
`(-1+5)/((-1-2)(-1+2))` =
`(4)/((-3)(1))` =
`(4)/(-3)` = -
`(4)/(3)`

(b)

The denominator of
`(g)/(h)` cannot be zero as this would make
`(g)/(h)` undefined

To find the values that x cannot be , equate the denominator to zero and solve for x

(x - 2)(x + 2) = 0

x - 2 = 0 ⇒ x = 2

x + 2 = 0 ⇒ x = - 2

values that are not in the domain of
`(g)/(h)` : x = - 2, x = 2