Understanding the Product Rule: Common Factor Simplification Confusion Explained

[fitz_calc]

I've already done the problem (here is the last part, sorry for crappy pic)

My question; if I multiply both sides of the + by x^2(x+1) / x^2(x+1) as the common factor to simplify the equation, then why does on of the x^2(x+1) disappear from the numerator in the final answer? It appears as though both denominators were used to simplify both sides of the +, yet only one numerator was used in the final calculation. Please tell me I'm not going crazy!

 

[EnumaElish]

Because the two terms in []'s on the first line are combined into a single [] on the second line.