Solve for 4/x+2 = 2/x x and determine if the solution is extraneous or not.
x = −2, extraneous
x = −2, non-extraneous
x = 2, extraneous
x = 2, non-extraneous

The given equation is:

4/(x + 2) = 2/x

First we get the value of x by doing cross multiplication so that all variables are in the numerator side:

4 x = 2 (x + 2)

4 x = 2 x + 4

2 x = 4

x = 2

An extraneous solution is one in which if we plug in the value of x back into the equation, the resulting values would be wrong.

Plug x = 2 back into the original equation:

4 / (2 + 2) = 2 / 2

4 / 4 = 2 / 2

1 = 1       (TRUE!)

Since the value of x = 2 satisfies the equation, then the solution is non-extraneous.

x = 2, non-extraneous

When the ball hit the ground, the height of the ball will be zero. So using the value of h(x) as zero in the given equation, we can find the time in which the ball will hit the ground.

0 = -(x-2)^2 + 16

(x-2)^2 = 16

x-2 = 16

x-2 = 4

x = 6

This means the ball will hit the ground 6 seconds after Amir threw it.