anonymous
  • anonymous
how would you solve this rational equation?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\sqrt{15x}(\sqrt{18x}+\sqrt{15x})\]
myininaya
  • myininaya
There is no equation to solve? Are you to multiply?
anonymous
  • anonymous
oops, it is supposed to be simplified!

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anonymous
  • anonymous
but that is the equation, I have the answer, but I am unsure how to get to it.
myininaya
  • 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
  • myininaya
Do you know how to multiply \[\sqrt{x} \cdot \sqrt{x}?\]
anonymous
  • anonymous
wouldn't that just be x?
myininaya
  • myininaya
right another question! Do you know the distributive property?
anonymous
  • anonymous
I do
myininaya
  • myininaya
so you know if you have a(b+c) you can do ab+ac
myininaya
  • myininaya
so you have \[\sqrt{15} \sqrt{x}(\sqrt{18} \sqrt{x}+\sqrt{15} \sqrt{x})\]
myininaya
  • myininaya
so you can treat the thing on the outside of the parenthesis just like that a above
anonymous
  • 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
  • anonymous
wait, I got it!!!
anonymous
  • anonymous
I think...
myininaya
  • 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
  • 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
  • myininaya
beautiful you didn't need my help
anonymous
  • 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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