Question

You are now a teacher, and you notice that many of your students are consistently making the dividing-out mistake that appears below. Some of the students even admit to knowing the method was wrong as soon as you point it out.
Create a visual to help your students stop making this common mistake: fraction numerator up diagonal strike x squared plus 3 x − 4 over denominator up diagonal strike x squared − 2 x − 8 end fraction .

Your lesson should do the following:

Explain why the dividing-out method is incorrect. You may want to start with a simpler expression and work your way up to polynomials. (For example, compare fraction numerator 3 left parenthesis 5 right parenthesis over denominator 3 end fraction and fraction numerator 3 plus 5 over denominator 3 end fraction.)
Explain when you can cancel a number that is in both the numerator and denominator and when you cannot cancel out numbers that appear in both the numerator and the denominator.
Share tricks, reminders, memory devices, or other methods to help students catch themselves before making this common mistake.
Post your video or series of images. Post answers to the following questions:

A. Why do you think the mistake shown here is such a common one?
B. Have you ever made this mistake before? What helped you stop making this mistake? What will help you stop making this mistake in the future?

Read and comment on the explanations of other student “teachers.”

A. Comment on ideas that helped you better understand or tricks to help you catch yourself before making the dividing-out mistake.
B. Ask a question to help a student improve his or her explanation or make it more thorough.

Respond to replies to your post.
Be sure to check back regularly to participate in the discussion with your fellow students and teacher.
P.S. I can not see pictures or videos that are posted on here, so if you could write everything out it would be kindly appreciated. :)

Answer 1

x to the 2nd power plus 3x-4

x to the 2nd power minus 2x-8

1. The dividing out method my seem like the thing to do but really you to to combine like terms on the top and the bottom so the top an the bottom should become 3x to the 2nd power plus (-4) over 2x to the 2nd power minus (-8) since you can only divide 3x to the 2nd power and 2x to the 2nd power your answer would become 3-4 over 2-8 because both x to the 2nd power cancelled each other out now minus the top and the bottom and the answer would be -1 over -6

2. for example (4)(6) over 4 plus 6 it would be hard to divide this because you the top and the bottom equations have not been solved yet, but when you do solve them your answer would be 24 over 10 but you cant divide these evenly   and when you do try to divide them you would get a decimal or 2.4 also your answer word be an improper fraction 24/10 which could change into 2 4/10nso i don't think is would be easy to divide in order not to make this mistake always make sure both the top and bottom equations are solved and make sure you can divide them  

3.a one thing i always remember is the equation solved yet i so can i divide

3.b What is the dividing out method can it be used for the following equation (3+4x) to the 2nd power over (4-2x) to the 2nd power.