If 𝑝

𝑞
= 𝑟
𝑠
, then 𝑝+𝑞
𝑟+𝑠
is equal to
A. 𝑝𝑠
𝑞𝑟
B.𝑝𝑞 − 𝑟𝑠
C. 𝑠
𝑞
D. 𝑞
𝑠

1 answer

By cross-multiplication we have 𝑝𝑠 = 𝑞𝑟. So we can substitute this in the expression 𝑝+𝑞/𝑟+𝑠 to get:

𝑝+𝑞/𝑟+𝑠 = (𝑝𝑠 + 𝑞𝑠) / 𝑟𝑠

Factor out 𝑠 in the numerator:

(𝑝𝑠 + 𝑞𝑠) / 𝑟𝑠 = 𝑠(𝑝+𝑞) / 𝑟𝑠

Using the fact that 𝑝𝑠 = 𝑞𝑟, we get:

𝑠(𝑝+𝑞) / 𝑟𝑠 = (𝑝+𝑞) / 𝑞

Therefore, the answer is (C) 𝑠/𝑞.