What is the difference start fraction r plus 2 over r plus 4 end fraction minus start fraction 3 over r plus 1 end fraction ?

1 answer

The difference is:

start fraction r plus 2 over r plus 4 end fraction minus start fraction 3 over r plus 1 end fraction =

(start fraction r plus 2 over r plus 4 end fraction) - (start fraction 3 over r plus 1 end fraction) =

[(r+2)/(r+4)] - [3/(r+1)] =

[(r+2)(r+1)]/[(r+4)(r+1)] - [3(r+4)]/[(r+1)(r+4)] =

[(r^2 + 3r + 2)/((r+1)(r+4))] - [(3r+12)/((r+1)(r+4))] =

[(r^2 + 3r + 2 - 3r - 12)/((r+1)(r+4))] =

[r^2 - 10)/((r+1)(r+4))]