Question

1.Two fellow students, Theo and Paula, have added two rational expressions. They ended up at different answers so they have asked you to check their work. Please explain to them any errors that you find. (Has attachments)

Answer 1

@ranga Help me plleeeaaaase?

Answer 2

Theo's mistake is in the second step where he multiplied the top of the expression on the left by (x+2). First of all it is not necessary to do that multiplication because the expression at the bottom (x-5)(x+2) is already the common denominator and therefore there is no need to multiply this expression by any factor. Secondly, any time you multiply the top you should also multiply the bottom to preserve the ratio. Theo only multiplies the top and not the bottom and therefore he has altered the ratio.

Paula's mistake is in the fourth step where she factors x^2-4x-5 into (x+2)(x-5) which is wrong factoring. Also, factoring is not needed here. Since the denominators of the two expressions is the same the numerator can be added. The mistake continues in the next step where she cancels out factors across an addition. You cannot do that. There is a plus sign between the two expressions and common factors cannot be cancelled out across addition or subtraction.

Answer 3

Oh, sweet, thanks, Ranga! Can you help me with two more questions, please?

Answer 4

Let us try one more.

Answer 5

Are you going to post them?

Answer 6

2.Wally knows that in order to add or subtract rational expressions, he has to find the least common denominator first. Unfortunately, he can not remember how to do that. Using complete sentences, explain to Wally how to find least common denominators. Make sure you clearly explain any important items to consider.

3.Wally is very thankful for your help, but he is still stuck. Describe to Wally how adding and subtracting rational expressions is similar to adding and subtracting simple fractions, and how they are different.

Answer 7

You can watch this video and put it in your own words:
http://www.virtualnerd.com/algebra-1/rational-expressions-functions/add-subtract/add-subtract-unlike-denominators/find-least-common-denominator-example

Answer 8

Here's the thing.. I have Parental Controls o the computer and mom won't remove them. :/ I can only go to certain sites, and that is not one of them. :(

Answer 9

@ranga you're doing a good job! :D

Answer 10

Least Common Denominator or LCD is the least common multiple of the denominators of two or more fractions. It is the smallest denominator that two or more fractions have in common. To find LCD do the following:
1) Factor each of the denominators.
2) Find the least common multiple among all the denominators. If the same factor occurs in all denominators, then the factor will occur only once in LCD. If a factor occurs in one denominator and not the other, then that factor has to go into the LCD. Once you find all the factors that go into the LCD, the product of the factors will be the LCD.
3) Once you find the LCD, make each fraction have the LCD in the denominator. You can do that by multiplying the numerator and denominator of each fraction by the same factor to make the denominator the same as LCD.
4) Once the LCD is the same, the numerator of each fractions can be added or subtracted and simplified.

Answer 11

Thanks PixieDust1.

Answer 12

Thank you, Ranga! I have to go for the night, but I'll be back tomorrow, and I'll reply, then.

Answer 13

For question 3) Adding and subtracting rational expressions is very similar to adding and subtracting simple fractions. In both cases you find the LCD, then multiply the top and bottom of each fraction by the same factor so that the bottom is same as the LCD. Once all fractions have the same LCD the top can be added or subtracted and then simplified. The method in each case is the same. In fractions we work with just numbers. In rational expressions we work with variables and numbers.

Alright. You are welcome.

Answer 14

Ah, thank you for all the help, Ranga. I really appreciate you putting up with my cluelessness every time I ask you for help.

Answer 15

You are welcome. Glad to be able to help.