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Mathematics 25 Online
OpenStudy (anonymous):

PLEASE HELP GUYS!? Find the lowest common denominator of 9/x+7-2/x :)

OpenStudy (tkhunny):

It is not clear what you intended. You wrote this: \(\dfrac{9}{x} + 7 - \dfrac{2}{x}\). Is that what you intended?

OpenStudy (anonymous):

no the x+7 is together sorry.

OpenStudy (ybarrap):

$$\tt \frac{9}{x}+7-\frac{2}{x}\\ $$ Find lowest denominator that goes with every factor: $$ \frac{9}{x}+\frac{7x}{x}-\frac{2}{x}\\$$ Ans: x

OpenStudy (anonymous):

\[\frac{ 9 }{ x+7 }-\frac{ 2 }{ x }\]

OpenStudy (tkhunny):

This is as I expected. Please use parentheses to group things. Remember your order of operations. \(\dfrac{9}{x+7} - \dfrac{2}{x}\) = 9/(x+7) - 2/x Do you see the difference from what you wrote? It is not a small thing.

OpenStudy (anonymous):

thats the question

OpenStudy (tkhunny):

What't a common denominator. Both denominators are prime, so there are limited choices.

OpenStudy (anonymous):

Wouldn't the common denominator just be 7x or something?

OpenStudy (tkhunny):

Or something. Just x(x+7). There is really no other reasonable choice.

OpenStudy (ybarrap):

The least common multiple of 1 and x is the common denominator. The 1 is the denominator for the 7 and x is for the others. "x" is the lowest factor between x and 1.

OpenStudy (ybarrap):

For example, what is the least common multiple between 12 and 18?

OpenStudy (ybarrap):

What is the smallest positive integer that is a multiple of each?

OpenStudy (tkhunny):

@ybarrap is still working the problem you originally posted. See how that notation was confusing?!

OpenStudy (ybarrap):

36. That is the lowest common multiple. And if it were in the denominator, it would be the lowest common denominator.

OpenStudy (anonymous):

Okay so I think for the original problem it'd just be x(x+7)

OpenStudy (ybarrap):

Least common multiple of (x+7,7)? What is it?

OpenStudy (ybarrap):

Nothing time x+7 gives 7 and nothing times 7 gives x+7, so x(x*7) is the least common multiple (i.e. lowest common denominator)

OpenStudy (anonymous):

Okay thank you so much, sorry about the misunderstanding in the beginning.

OpenStudy (tkhunny):

* (x+7) of course.

OpenStudy (ybarrap):

right *x(x+7), thanks.

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