Question: I am trying to decipher the steps needed to determine the intersection point between curves represented by the two following equations:

$$y= 2\;x+2$$

$$y= \dfrac{128}{(x+1)^2}$$

I know that they intersect at the point (3,8), but I am unsure of whether I should get rid of the denominator first when starting the process. Could someone please work out the project so I can understand how to arrive at this point?

Answer: 
One cannot "remove" the denominator of an expression. You want to equate the two expressions and then solve for $x$. So, start with $2x + 2 = \frac{128}{(x+1)^2}$.
Note that $(x+1)$ is common factor . So, set it equal to u.

$$ y= 2 u = 128/u^2 \rightarrow( 2 u^3 = 128) \rightarrow ( u= 4 ) \rightarrow (x=3, y= 8) $$