Question

solve for R? R(r^1+r^2)+r^1r^2

Answer 1

Is this your question?
\(R(r^1+r^2)+r^1r^2\)
You really can solve this for anything since it is an expression - there is no equal sign.

Answer 2

I meant "can't solve this" - sorry.

Answer 3

oops i typed it wrong its \[R(r ^{1}+r ^{2})=r ^{1}r ^{2}\] @gypsy1274

Answer 4

Much Better. R and r are two different variables?

Answer 5

yes i distributed them but now i dont know where to go

Answer 6

Sorry, my mistake. Don't distribute. You need to separate the R from the parenthesis using inverse operations.

Answer 7

You also need to combine the \(r^1r^2\) - do you know how to do that?

Answer 8

so what i divide the R on both sides? no i dont think i do would i just add the exponents?

Answer 9

The \(r^1r^2\) is being multiplied so yes, you will add the exponents.
You want R to be by itself so it is not what you will be dividing.

Answer 10

ok so i would divide by \[r^{1}+r ^{2}\] and add the exponents of the others to get R= \[r ^{3}\div r ^{1}+r ^{2}\]

Answer 11

You've got the right idea, but don't forget the parenthesis - they will change the answer.
\(R=r^3\div(r^1+r^2)\)
Next is to simplify.

Answer 12

how could it be simplified anymore than that?

Answer 13

Do you have answer choices? I don't want to lead you down the wrong path here and I'm not completely sure that my simplification is correct.

Answer 14

\[r=\frac{r^3}{r+r^2} = \frac{r^3}{r}+\frac{r^3}{r^2} = r^2+ r\]
The more I think about it, the less I like it.
@e.mccormick @uri What are your thoughts?

Answer 15

no or else i would have probably gotten the answer on my own haha but i put it into mathway and it got \[R=\frac{ r ^{2} }{ r+1 }\]

Answer 16

its sad how all these problems i have to do are like this the exponents are what throw me off >.<

Answer 17

I got it! Give me a minute to explain it.

Answer 18

\(\dfrac{r^3}{r(1+r)}\) When you divide a term with the same base and different exponents, you subtract the exponents. So... After factoring out the r you divide \(r^3\) by \(r\) leaving you with:
\(R=\dfrac{r^2}{r+1}\)

Answer 19

THank you for asking this question. I have learned something today.

Answer 20

wait but where is this 1 coming from?

Answer 21

When you factor out the r from the denominator, \(r \div r = 1\)

Answer 22

Order doesn't matter with addition so \(1+r = r+1\)

Answer 23

ohhhhhhh ok thank you so much!

Answer 24

Your welcome.

Answer 25

Yah, any single variable can be said to be one of itself. So \(x = 1x\), \(r=1r\) and so on. That is the reason why the factoring works. One is a number that likes to hide and take on special forms.

\(\frac{x}{x}=1\) is a principal you can use to multiply by one, changing nothing mathematically, but changing an equation dramatically. I just point this out for future use! it comes in handy when doing this type of work with fractions.