Question

The password for a certain safe is indicated by multiplying (x^2-16)/(x-1) with 1 / ((x ^ 2 + 6x + 8) / (x ^ 2 + 2x-3)) . Knowing that the value of X = 9. What is the numeric value of the password.

Answer 1

5.455

Explanation:

If the password for a certain safe is indicated by multiplying (x^2-16)/(x-1) with 1 / ((x ^ 2 + 6x + 8) / (x ^ 2 + 2x-3))

Simplify the expression in its lowest term first

`= (x^2-16)/(x-1) * (1)/((x ^ 2 + 6x + 8)/(x ^ 2 + 2x-3) ) \\\\= (x^2-16)/(x-1) * }{(x ^ 2 + 2x - 3)/(x ^ 2 + 6x + 8) }\\\\= ( (x+4)(x-4))/(x-1) * ((x+3)(x-1))/((x+4)(x+2))\\\\= (x-4)/(1) * (x+3)/(x+2)\\`

If the value of x = 9, to get the numeric value of the password, we will substitute x = 9 into the resulting function as shown;

`= (x-4)/(1) * (x+3)/(x+2)\\\\= (9-4)/(1) * (9+3)/(9+2)\\\\= (5)/(1) * (12)/(11)\\\\= (60)/(11)\\ \\= 5.455`

Hence the numeric value of the password is 5.455