Question

1. Two fellow students, Theo and Paula, have added two rational expressions. They ended up with different answers, so they have asked you to check their work. Please explain to them any errors that you find.
2.
Wally knows that in order to add or subtract rational expressions, he has to find the least common denominator first. Unfortunately, he cannot 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.

Answer 1

For problem 1., you need to show the work Theo and Paula did.

Answer 2

@mathstudent55

Answer 3

Let's look at each line.
Line 1. They both start with the same problem
Line 2. They both factor the left denominator correctly.
Ok so far?

Answer 4

In line 3 we see a difference between their work.

Answer 5

The LCD is (x - 5)(x + 2)
Since the left fraction has a denominator of (x - 5)(x + 2), it already has the LCD, so Theo made a mistake in Line 3 of writing (x + 2) in the numerator of the left fraction.

Answer 6

From Line 3, Theo's answer is incorrect.

Answer 7

In Line 3, Paula left the left fraction alone (which is correct) and multiplied the right fraction by (x + 2) over (x + 2) to have the LCD. That is correct.

Answer 8

So Paula did it right?

Answer 9

In Line 4, Paula FOILed the numerator of the right fraction correctly, so in Line 4 Paul is still correct.

Answer 10

To answer your question, we need to follow Paula's answer to the end to see if there is any error at any point. Up to Line 4, Paula is correct. That's all we know so far.

Answer 11

In Line 5, Paula flipped the second fraction. To do an operation with fractions. the only time you flip the second fraction is when you are dividing fractions. You don't flip the second fraction in an addition, so Paula's answer is incorrect starting with the 5th Line.

Answer 12

This is how Paula should have continued:
Line 5. \(\dfrac{(2x + 5) + (x^2 -4x - 5) }{(x - 5)(x + 2) } \)

Answer 13

Line 6: \(\dfrac{2x + 5 + x^2 -4x - 5 }{(x - 5)(x + 2) } \)

Answer 14

Line 7: \(\dfrac{x^2 -2x }{(x - 5)(x + 2) } \)

Line 8: \(\dfrac{x(x -2) }{(x - 5)(x + 2) } \)

Answer 15

Lines 7 and 8 are both acceptable as a final correct answer.

Answer 16

Alright thank you sooo much

Answer 17

You're welcome.

Answer 18

Can you help me with number 2?

Answer 19

2.
The first step is to factor all denominators.
Then you need to find the LCD of the denominators. For that you need one factor of each of all the factors present in all denominators. If there are two factors that are the same, take the one to the higher power.