rational expressions

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Question Description

1. How is multiplying/dividing rational expressions similar to multiplying/dividing fractions? How is adding/subtracting rational expressions similar to adding/subtracting fractions?

2. How do you solve rational equations?

3. In the rational expression, 4x 8x2+4x 12 , why is it incorrect to cancel the 4x in the numerator with the 4x in the denominator? How would you correctly simplify this rational expression?

Tutor Answer

vmohanakumar
School: UC Berkeley

I am fine too.I finished it. Please take a look. Let me know if you need more details or any modification.

1. How is multiplying/dividing rational expressions similar to multiplying/dividing fractions?
How is adding/subtracting rational expressions similar to adding/subtracting fractions?
When we multiply fractions, we multiply the numerators and multiply the denominators. That is
𝑎 𝑐

𝑎𝑐

𝑏 𝑑

𝑏𝑑

. =

, 𝑤ℎ𝑒𝑟𝑒 𝑎, 𝑏, 𝑐, 𝑎𝑛𝑑 𝑑 𝑎𝑟𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟𝑠 𝑎𝑛𝑑 𝑏 𝑎𝑛𝑑 𝑑 ≠ 0, then we simplify the result by cancelling

the common factor. We multiply rational expressions the same manner. Multiply the numerators and
denominators, factor both the numerator and denominator of the product, and cancel common
factors.
𝑝(𝑥) 𝑟(𝑥)

That is 𝑞(𝑥) . 𝑠(𝑥) =

𝑝(𝑥)𝑟(𝑥)
𝑞(𝑥)𝑠(𝑥)

, 𝑞(𝑥)...

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