We can start by cross-multiplying the original equation to get 𝑝𝑠 = 𝑞𝑟. Then, we can use this to manipulate the expression 𝑝+𝑞
𝑟+𝑠:
𝑝+𝑞
𝑟+𝑠 = (𝑝+𝑞) / (𝑟+𝑠) (dividing both numerator and denominator by 𝑝𝑠)
= (𝑝/𝑝𝑠 + 𝑞/𝑝𝑠) / (𝑟/𝑝𝑠 + 𝑠/𝑝𝑠)
= (𝑠/𝑞 + 1) / (𝑟/𝑝 + 1) (using 𝑝𝑠 = 𝑞𝑟)
At this point, none of the answer choices match exactly, so we can simplify further:
(𝑠/𝑞 + 1) / (𝑟/𝑝 + 1)
= (𝑠 + 𝑞) / (𝑞(𝑟/𝑝) + 𝑞)
= 𝑝𝑠/𝑞𝑟 + 𝑝/𝑞
The only answer choice that matches this expression is A, so the answer is A.
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