Question

How do you add or subtract `(x+6)/(5x+10) - (x-2)/(4x+8)`?

Answer 1

Notice that the denominator of each of these terms is a simple multiple of `(x+2)`, so we only need to multiply by constants to make the denominators of the two terms the same:

`(x+6)/(5x+10)-(x-2)/(4x+8)`

`=(x+6)/(5(x+2))-(x-2)/(4(x+2))`

`=(4*(x+6))/(4*5(x+2))-(5*(x-2))/(5*4(x+2))`

`=(4(x+6))/(20(x+2))-(5(x-2))/(20(x+2))`

`=(4(x+6)-5(x-2))/(20(x+2))`

`=(4x+24-5x+10)/(20(x+2))`

`=(14-x)/(20(x+2))`

`=(14-x)/(20x+40)`