Find the indicated sums and differences. 3/x + 5 - 2/x - 3?

2. Find the indicated sums and differences. x+5/3 - x-3/2.


3. Find the indicated sums and differences. 3/a-5 + a+2/a.


4. Find the indicated sums and differences. 3k/k-2 + 6/2-k.


5. Find the indicated sums and differences. b+1/b+2 - b+3/b+4.


Thanks so much.

Find the indicated sums and differences. 3/x + 5 - 2/x - 3?
Okay:





1. Multiply each fraction by the missing denominator. In other words, for the first one, multiply top and bottom by (x-3). Your common denominator here is (x+5)(x-3). So, you get 3x-9-2x-10 all over (x+5)(x-3). So, combine like terms and you get x-19 / (x+5)(x-3)





2. Similar: Instead, multiply each fraction by the missing constant that makes it a common denominator, this case 6. So, multiply the first one top and bottom by 2 and the second one by 3. You get 2x+10-3x+9 all over 6. You get in the end: -x+19 or 19-x / 6.





3. Similar again: multiply the first fraction top and bottom by a and the second one by a-5. So you get 3a+a^2-3a-10 all over a(a-5). Combining like terms, you get a^2-10 over a^2-5a. Notice here if you factor out an a from top and bottom, look what happens: a(a-5) over a(a-5) so these both cancel and you get 1 as your answer.





4. For this one, multiply the second term first by -1. This will make them identical denominators, and then combine:





3k-6 / k-2. Then simplify by factoring out a 3: 3(k-2)/k-2 or 3.





5. Multiply each fraction, as in the earlier problems, by the missing denominator: b^2+5b+4-b^2-5b-6 all over (b+2)(b+4). You can cancel a lot here and you are left with -2 / (b+2)(b+4)