Çözüldü Algebraic Simplification - Rational Fractions

If x, y, z are real numbers, x + y + z = 30, and 1 / (x + y) + 1 / (x + z) + 1 / (y + z) = 13 / 5,
x / (y + z) + y / (x + z) + z / (x + y) = ?

A) 75
B) 72
C) 64
D) 60
E) 54

y + z = 30 - x, x + y = 30 - z, x + z = 30 - y
x / (y + z) + y / (x + z) + z / (x + y) =
[ 30 - (30 - x) ] / (30 - x) + [ 30 - (30 - y) ] / (30 - y) + [ 30 - (30 - z) ] / (30 - z) =
[ 30 / (30 - x) ] - 1 + [ 30 / (30 - y) ] - 1 + [ 30 / (30 - z) ] - 1 =
30 / (30 - x) + 30 / (30 - y) + 30 / (30 - z) - 3 =
30·[ 1 / (30 - x) + 1 / (30 - y) + 1/ (30 - z) ] - 3 =
30·[ 1 / (y + z) + 1 / (x + z) + 1 / (x + y) ] - 3 =
30·(13 / 5) - 3 =
6·13 - 3 =
3·(2·13 - 1) =
3·(26 - 1) =
3·25 =
75.

Source (Turkish): https://numunekitap.com/paraf/ayt/ayt-matematik-konu-takip-denemeleri#p=4
(Question 1 with no answer key)