Jamierox4ev3r
  • Jamierox4ev3r
Math Review Day 3! 6e. Rationalize the expression and simplify.
Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
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Jamierox4ev3r
  • Jamierox4ev3r
Let me re-type the question 6e. Rationalize the expression and simplify \(\huge\frac{\sqrt{4+h}-2}{h}\)
anonymous
  • anonymous
Is this root just for 4? Or h also?
Jamierox4ev3r
  • Jamierox4ev3r
the root is \(\sqrt{4+h}\) @joyraheb

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Nnesha
  • Nnesha
i guess multiply the numerator and the denominator by the `conjugate` of the numerator
Jamierox4ev3r
  • Jamierox4ev3r
I do believe that the first step would be to multiply the whole expression by the conjugate of the numerator. So I assume that it would look a little like this: \(\huge\frac{\sqrt{4+h}-2}{h}\times\huge\frac{\sqrt{4+h}+2}{\sqrt{4+h}+2}\)
Jamierox4ev3r
  • Jamierox4ev3r
LOL you read my mind XD There is a lot of multiplying of conjugates in Algebra. A common trend that I recall
Jamierox4ev3r
  • Jamierox4ev3r
If you multiply these, you should get \(\huge\frac{(4+h)-4}{h(\sqrt{4+h}+2}\) right?
Nnesha
  • Nnesha
yes right!
Jamierox4ev3r
  • Jamierox4ev3r
yes! oops wait i think a parentheses is missing in in the denominator \(\huge\frac{(4+h)-4}{h(\sqrt{4+h})+2}\)
Jamierox4ev3r
  • Jamierox4ev3r
anyhow, from here I'm a little stuck. I know the in the numerator, 4 and -4 cancel out, so you're left with h...but what happens in the denominator?
Nnesha
  • Nnesha
yes right \(\huge\rm \frac{\color{reD}{4}+h\color{reD}{-4}}{h(\sqrt{4+h}+2)}\)\[\rm \frac{ h }{ h(\sqrt{4+h}+2)}\] can you cancel out anything ?
Jamierox4ev3r
  • Jamierox4ev3r
oh wait! i see. So i mentioned canceling out in the numerator, but it seems like something in the numerator and denominator can be cancelled out \(\huge\rm \frac{\color{reD}{4}+\color{green}h\color{reD}{-4}}{\color{green}h(\sqrt{4+h}+2)}\) The things in green become 1, so wouldn't you have this: \(\huge\frac{1}{\sqrt{4+h}+2}\)
Nnesha
  • Nnesha
parentheses should be aftr 2 cuz it's one expression (sqrt{4+h}+2)
Nnesha
  • Nnesha
that's right!
Jamierox4ev3r
  • Jamierox4ev3r
oh true, whoops XD and ty ;-;
Nnesha
  • Nnesha
np don't cry:(
Jamierox4ev3r
  • Jamierox4ev3r
yeah i put the parentheses in the wrong place earlier. my bad hehe I'm fine. From there, am I done?
Jamierox4ev3r
  • Jamierox4ev3r
is that the final answer?
Nnesha
  • Nnesha
btw do you have the answer ? just want to know cuz most of times we r not allowed to leave the square root at the denominator
Nnesha
  • Nnesha
yes i think so we can't do anything else with that exprssion
Jamierox4ev3r
  • Jamierox4ev3r
hmmm lemme check online. The textbook doesn't have the answers in it, but the textbook's website has them. Brb
Nnesha
  • Nnesha
oh cool
Jamierox4ev3r
  • Jamierox4ev3r
Yep that's it. Thank you thank you! XD
Nnesha
  • Nnesha
my pleasure

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