Simplify This Fraction

- anonymous

Simplify This Fraction

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- anonymous

|dw:1377728653372:dw|

- anonymous

Have you learned the keep, change, flip method?

- anonymous

Never heard of it!

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## More answers

- anonymous

Ok, I'll teach you. First, we keep the top fraction as it is.

- anonymous

Next, we change the division sign to a multiplication sign.
So this will look like "fraction 1" x "fraction 2"

- anonymous

step 3 is to Flip the bottom fraction. In this case you have bottom fraction 1+ bottom fraction 2, so you would flip both of them.

- anonymous

so 10/x+1 x 2/1 x+1/3?

- anonymous

close. \[(10/x+1)(2/1+ x+1/3)\]

- anonymous

you aren't multiplying the last two fractions; maybe you just missed the + sign in between?

- anonymous

Oh I get it, so what do you do next? Now that I have (10/x+1)(2/1 + x+1/3)?

- anonymous

now we need to get a common denominator for the second term.
so in other words, how can we change the expression \[(2/1 + (x+1)/3) \] to have a common denominator?

- anonymous

Hmm, you have to find the GCF for the denominators right?

- anonymous

Well 2/1 has a denominator of 1, so 2/1=2. (x+1)/3 has a denominator of 3. So if we want 2/1 to have a denominator of 3, what we do to the top, we must do to the bottom, so what would the top become?

- anonymous

6 right? Because you have to multiply 3 to the bottom and top?

- anonymous

Ok, so now we have (10/x+1)(6/3+(x+1)/3). Now we can combine the numerators in the right hand term since they both have a denominator of 3. What do you get?

- anonymous

3+x/3? and you would just cancel out the 3 and be left with (10/x+1)(x)?

- anonymous

not exactly. Let's look at the second term only.
we have (6/3 + (x+1)/3). So if 6 and x+1 are our numerators, we can add them together because they have the same denominator. What do you get?

- anonymous

Woops, I looked at my work wrong. You would just have 7+x/3

- anonymous

Actually. I have a much easier way. Don't hate me, but it's simpler to do it the second way in this case.

- anonymous

ok, so starting from the beginning, we have two different denominators. one of them is 2 and one of them is x+1. go through each fraction individually and make it so that the denominator is 2(x+1)...don't multiply anything out yet, just leave it as multiplication and let me know what you get. remember that what you do to the top, you must do to the bottom.

- anonymous

Would it be |dw:1377730424737:dw|

- anonymous

are you starting from the beginning?

- anonymous

Yeah, I multiplied the 1 and the 2 in 1/2 by (x+1) and I multiplied the 3/x+! by 2

- anonymous

|dw:1377730550847:dw|

- anonymous

Yeah that is what I did

- anonymous

Ok, so now you see from the attached example that all of the smaller fractions have the same denominator. When all fractions have a common denominator, we can eliminate the denominators from the problem and work with the numerators. So if we cross out all of those denominators, what are we left with?

- anonymous

20/7+x?

- anonymous

perfect!

- anonymous

sorry for the confusion on the first part!

- anonymous

It's alright! It was worth it in the end, I actually kinda understand now. Thanks!

- anonymous

okay good! let me know if you have any questions!!

- anonymous

Will do!

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