Question 421455
production rate of first factory is (x+21) / (2x*(x+5))
production rate of second factory is (9x+16) / (2x*(x+5))


product rate of both factories combined is additive and equals:

((x+21) / (2x*(x+5))) + ((9x+16) / (2x*(x+5))) = ((x+21) + (9x+16)) / (2x*(x+5))


the fractions can be combined because the denominators are the same.


you can then simplify by combining like terms to get:


combined rate of production equals (10x + 37) / (2x*(x+5))


here's how combining production rates work.


i can product 5 widgets an hour.
you can produce 10 widgets an hour.

together we can produce 15 widgets an hour (my 5 per hour plus your 10 per hour).