Question

How do you do this math problem?

Answer 1

You can simply add the fractions in the most straightforward way, then reduce the result.

`(2)/(3x^(2)+12x)+(8)/(2x) = ((2(2x)+8(3x^(2)+12x))/((3x^2+12x)(2x))`

`= (24x^(2)+100x)/(6x^(2)* (x+4)) = (2(6x+25))/(3x(x+4))`

Or, you can reduce and factor the given fractions, find a common denominator, and use that.

`(2)/(3x(x+4))+(4)/(x) = (2+4(3(x+4)))/(3x(x+4)) =(12x+50)/(3x(x+4))`

Either way, the expanded (some would say "simplified") result is

`(12x+50)/(3x^(2)+12x)`