simplify (9/m) - (3+m/2m) + (5/2)?

Question

answers:
11+m
15-4m
15+4m/2m
6+4m

Answer 1

take 2m as the LCD

18-3-m+5m/2m
15+4m/2m---answer

Answer 2

We definitely want to get rid of the fractions, so we'll multiply by the least common multiple(LCM) of the denominators. m, 2m, and 2 have an LCM of 2m, so that's what we'll multiply the entire expresison by.

9/m - (3 + m)/2m + 5/2

2m[9/m - (3 + m)/2m + 5/2]
18m/m - (6m + 2m^2)/2m + 10m/2
18 - (3 + m) + 5m
18 - 3 - m + 5m
15 + 4m

The multiplication could be done in an easier way, but it's tough to type it in here. After distributing the 2m, all fractions will go away. Careful in step 3 to 4 where the last set of parenthesis goes away, you need to distribute that minus sign to both the 3 and the m. Good luck!