Need Help! Simplifying Expressions...?

Question

m squared + n squared over m squared - n squared +(plus)+ m over n-m +(plus) n over m + n


5 over x squared - 3x - 28 +(plus)+ 7 over 2x + 14


1 over h squared - 9h + 20 -(minus) 5 over h squared - 10h + 25


1 over b + 2 +(plus)+ 1 over b - 5 over 2 b squared - b - 3
over b squared - 3b - 10


Help with any of these would be great! THANK YOU!

Answer 1

(m^2+n^2)/(m^2-n^2) + m/(n-m) + n/(m+n) =
(m^2 + n^2)/((m+n)(m-n)) - m/(m-n) + n/(m+n) =
((m^2+n^2) - m(m+n) + n(m-n))/((m+n)(m-n)) =
(m^2 +n^2 -m^2 +mn + mn -n^2)/((m+n)(m-n))=
2mn/((m+n)(m-n))

Answer 2

1 over h squared - 9h + 20 -(minus) 5 over h squared - 10h + 25
1/((h - 5)(h - 4) - 5/(h - 5)^2 =
(h - 5 -5(h - 4))/((h - 4)(h - 5)^2) =
(-4h + 16)/((h - 4)(h - 5)^2) =
-4(h - 4)/((h - 4)(h - 5)^2) =
-4/(h - 5)^2

Answer 3

Basically, you are just adding. The things you are adding are rational expressions, fractions, so just look for the common denominator in each.
For example, the common denominator for the first problem is (-1), (m+n) and (m-n), a collection of the factors or each denominator (the maximum times that each factor appears but in this case they just appear once).
Use the common denominator to add these fractions.
That is what you are going to do with each of these problems.