Question

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

Answer 1

[AI-generated answer — Bot]

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.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To simplify the expression 𝑝+𝑞/𝑟+𝑠, we need to follow the order of operations, which is called BIDMAS or PEMDAS. According to this rule, we need to do the division first, followed by addition.

So, let's simplify the expression step by step:

Step 1: Simplify 𝑞/𝑟
Since 𝑞/𝑟 is division, we can rewrite it as 𝑞 * 1/𝑟 (multiplication by the reciprocal).
Therefore, 𝑞/𝑟 = 𝑞 * 1/𝑟 = 𝑞/𝑟

Step 2: Simplify 𝑝+𝑞/𝑟+𝑠
Now, substituting the values we found in Step 1, we get:
𝑝+𝑞/𝑟+𝑠 = 𝑝 + (𝑞/𝑟) + 𝑠

Step 3: Simplify 𝑝 + (𝑞/𝑟) + 𝑠
Since 𝑝 + (𝑞/𝑟) + 𝑠 involves addition, we can combine the terms with the same variables (𝑝 and 𝑠). However, we cannot combine the term 𝑞/𝑟 with 𝑝 or 𝑠 because they have different variables.
Therefore, 𝑝 + (𝑞/𝑟) + 𝑠 cannot be simplified further.

So, the answer is 𝑝+𝑞/𝑟+𝑠.