how would you solve this rational equation?

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- anonymous

how would you solve this rational equation?

- jamiebookeater

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- anonymous

\[\sqrt{15x}(\sqrt{18x}+\sqrt{15x})\]

- myininaya

There is no equation to solve?
Are you to multiply?

- anonymous

oops, it is supposed to be simplified!

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## More answers

- anonymous

but that is the equation, I have the answer, but I am unsure how to get to it.

- myininaya

So we want to simplify the expression.
Again there is no equation.
Just so you know assuming we have x>=0
you can write \[\sqrt{18x}=\sqrt{18} \sqrt{x}\]
and you can also do the same for the other terms too.

- myininaya

Do you know how to multiply \[\sqrt{x} \cdot \sqrt{x}?\]

- anonymous

wouldn't that just be x?

- myininaya

right
another question!
Do you know the distributive property?

- anonymous

I do

- myininaya

so you know if you have a(b+c) you can do ab+ac

- myininaya

so you have
\[\sqrt{15} \sqrt{x}(\sqrt{18} \sqrt{x}+\sqrt{15} \sqrt{x})\]

- myininaya

so you can treat the thing on the outside of the parenthesis just like that a above

- anonymous

yes, but wouldn't all of the square roots cancel out? I tried this but the answer i received had no square roots in it. But the answer that is given does...

- anonymous

wait, I got it!!!

- anonymous

I think...

- myininaya

Is 15*18 a perfect square?
I don't think it is.
So you would have at least one square root in your answer.
What do you think the answer is?

- anonymous

well, the given answer is
\[3x \sqrt{30} +15x\]
so first I simplified what i could inside the parenthesis and got
\[\sqrt{15x} (3\sqrt{2x} + \sqrt{15x})\]
and then I distributed (Like you said!) and got this
\[3\sqrt{30x ^{2}} + \sqrt{15^{2}x ^{2}}\]
then I canceled out the roots (like you said) and got the answer!

- myininaya

beautiful
you didn't need my help

- anonymous

I did! If I hadn't had it I probably would have given up (as cliche as that sounds) Thank you so much for working me through it!

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