To simplify rational expressions, it is often helpful to factor all of the involved polynomials:
(1)
10/(x^216x+60) + 7/(x^2100)
= 10 /[(x6)(x10)] + 7/[(x10)(x+10)]
Since both terms in the expression have an (x10) in the denominators, we only need an extra (x6) in the first term and an (x+10) in the second. Now, we cannot willynilly add terms to products, but we can multiply expressions by 1 and preserve them. To wit:
10(x+10) /[(x6)(x10)(x+10)] + 7(x6)/[(x10)(x+10)(x6)]
= (10x+100)/[~] + (7x42)/[~] (I am using ~ for the common denominator.)
= (10x+100 + 7x42)/[~] (We can add two fractions since we have a common denominator.)
= (17x+58)/[(x6)(x10)(x+10)]
For your second expression, please verify the first denominator as I presume you added an x in there.
11/28/2013

Jonathan G.