Question

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.

Answer 1

@ganeshie8

Answer 2

My teacher said "Great work! Please check Paula's work again to find her error. Remember, she is adding the rational expressions."

Answer 3

@freckles ganeshie told me to tag you :p

Answer 4

So do you know you can cancel common factors over division not addition?

Answer 5

for example,
(assume x doesn't equal 0)
\[\frac{x}{x}+\frac{x}{x} \text{ doesn't equal } \frac{x}{\cancel {x}}+\frac{ \cancel{x}}{x}=x+\frac{1}{x} \\ \frac{x}{x}+\frac{x}{x}=1+1=2 \]

Answer 6

I thought you could cancel common factors in any type of problem like subtraction, addition, division, and multiplication?

Answer 7

nope

Answer 8

another example
\[\frac{2}{2}+\frac{2}{2} =1+1=2 \\ \text{ but you cannot say } \\ \frac{2}{2}+\frac{2}{2}=\frac{2}{1}+\frac{1}{2}=2+\frac{1}{2} \]

Answer 9

do you see how 2 and 2+1/2 are not the same ?

Answer 10

so you cannot cancel common factors over addition and/or subtraction

Answer 11

@CrazyTurtle483 do you understand the example?

Answer 12

one is showing what you can do
the other part of the example is showing what you cannot do

Answer 13

Yes I do

Answer 14

So is that the error in Paula's problem? That she canceled over addition?

Answer 15

@freckles