Question

Simplify the expression and rationalize the denominator

\[\frac{1}{sqrt{t}}(\frac{1}{sqrt{t}}-1)\]

Answer 1

\[\frac{1}{\sqrt{t}}(\frac{1}{\sqrt{t}}-1)\]

Answer 2

The answer is... \[\frac{1-\sqrt{t}}{t}\]

Answer 3

\[\frac{1}{\sqrt{t}}(\frac{1}{\sqrt{t}}-1)\]\[=\frac{1}{\sqrt{t}}(\frac{1}{\sqrt{t}}-\frac{\sqrt{t}}{\sqrt{t}})\]\[=\frac{1}{\sqrt{t}}(\frac{1-\sqrt{t}}{\sqrt{t}})\]\[=\frac{1-\sqrt{t}}{\sqrt{t}(\sqrt{t})}\]\[=...?!\]

Answer 4

But I got... \[\frac{t-t \sqrt{t}}{t}\]

Answer 5

Can you show your steps?

Answer 6

I multiplied the coefficient in front first instead of doing what you did inside first:
\[\frac{1}{t}-\frac{1}{\sqrt{t}}\]
\[\frac{\sqrt{t}-t}{t\sqrt{t}}\]
\[\frac{\sqrt{t}-t}{\sqrt[3]{t^2}}*\frac{\sqrt[3]{t^2}}{\sqrt[3]{t^2}}\]
And then the answer I got...

Answer 7

\[t\sqrt{t} = \sqrt[2]{t^3}\]

Answer 8

Woops yeah but now my answer is even mre wrong...\[\frac{\sqrt{t}-t}{t^2}\]

Answer 9

Let me try to do it using your method.
\[\frac{1}{\sqrt{t}}(\frac{1}{\sqrt{t}}-1)\]\[=\frac{1}{t}-\frac{1}{\sqrt{t}}\]\[=\frac{\sqrt{t}}{t\sqrt{t}}-\frac{t}{t\sqrt{t}}\]\[=\frac{\sqrt{t}-t}{t\sqrt{t}}\]\[=\frac{\sqrt{t}(1-\sqrt{t})}{t\sqrt{t}}\]\[=\frac{1-\sqrt{t}}{t}\]

Answer 10

\[= \frac{1}{t} - \frac{1}{\sqrt{t}} = \frac{1 - \sqrt{t}}{t}\]

Answer 11

I don't understand after your second to last line

Answer 12

\[=\frac{\sqrt{t}}{t\sqrt{t}}-\frac{t}{t\sqrt{t}}\] This？

Answer 13

I think there is no need of rationalizing the denominator by LCM we can make the denominator rational..

See. first distribute 1/root(t)..

Then take the LCM you have your answer..

Answer 14

@waterineyes You're skipping too many steps.

Answer 15

What what is the need of doing that steps??

First distribute:
\[\frac{1}{t} - \frac{1}{\sqrt{t}}\]

Now the LCM is t and solve further..

Answer 16

If the asker understands, that's fine.

Answer 17

If the asker does not understand then I will explain it more..

Answer 18

So, now, it's time to check if @purplec16 understands.

Answer 19

I am a visual learner. And I don't understand how you rationalize the denominator and where you got the square of t to take out from the numerator

Answer 20

Can I explain you what Callisto did??

Answer 21

Sure :D

Answer 22

Tell me callisto's which step you are not getting??

Answer 23

The last two

Answer 24

In which reply of Callisto, there are these two steps??

Answer 25

Let me try to do it using your method.

In this reply or his earlier own reply??

Answer 26

Before \[=\frac{\sqrt{t}(1-\sqrt{t})}{t\sqrt{t}}\]add a step, so it becomes
\[=\frac{\sqrt{t}-(\sqrt{t})(\sqrt{t})}{t\sqrt{t}}\]\[=\frac{\sqrt{t}(1-\sqrt{t})}{t\sqrt{t}}\]

Answer 27

It's taking out the common factor.

Answer 28

I see it now... but how do you rationalize...

Answer 29

See, callisto has taken root(t) common there and it will cancel with root(t) in the denominator..

Answer 30

I cross out the common factor. root(t)

Answer 31

You have problem in here in rationalising or you don't know about rationalising??

Answer 32

o.O...

Answer 33

I know..

Answer 34

\[=\frac{\sqrt{t}(1-\sqrt{t})}{t\sqrt{t}}\]\[=\frac{\cancel{\sqrt{t}}(1-\sqrt{t})}{t\cancel{\sqrt{t}}}\]\[=\frac{(1-\sqrt{t})}{t}\]

Answer 35

Cool... Thanks so much both!!!... my way is harder I think I will try to remember to use yours.

Answer 36

Not to remember, but to understand. When you understand, you can use it easier. When you remember, you may forget.