The given expression is:
3
(a-3) (a-5)
1
1
1
(a - 3) (a - 4) (a-4) (a - 5) (a - 5 ) (a - 3)
Simplifying the denominators, we get:
3
(a-3) (a-5)
1
1
1
(a - 3) (a - 4) 4(a - 5)^2 3(a - 3)(a - 5)
Now, we can find the least common denominator, which is:
4(a - 5)^2 (a - 4) 3(a - 3)(a - 5)
Multiplying the first term by 4(a - 5)^2 and simplifying, we get:
12(a - 4)
Multiplying the second term by 3(a - 3) and simplifying, we get:
3(a - 4)
Multiplying the third term by 4(a - 4)(a - 5)^2 and simplifying, we get:
4
Multiplying the fourth term by (a - 5)(a - 3)(a - 4)(a - 5)^2 and simplifying, we get:
(a - 3)(a - 5)
Multiplying the fifth term by (a - 4)(a - 3)(a - 5)(a - 5) and simplifying, we get:
1
Adding all the simplified terms, we get:
12(a - 4) + 3(a - 4) + 4 + (a - 3)(a - 5) + 1
4(a - 5)^2 (a - 4) 3(a - 3)(a - 5)
Simplifying further, we get:
15a - 57
12(a - 5)^2