formula simplification

dennyloi

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Joined
Jan 4, 2014
Messages
8
I have 2 equations that I want to multiply together then simplify as follows:

1: a/t

2: t(d-t) / ad

I am told it simplifies to:
1 - (t/d)

I am looking for some help with the intermediate steps.

Thanks
 
I have 2 > > equations < < that I want to multiply together then simplify as follows:

They are expressions, not equations.

1: a/t

2: t(d-t) / ad \(\displaystyle \ \ \ \ \) t(d - t)/(ad) <------- You need grouping symbols around the denominator.

I am told it simplifies to:
1 - (t/d)

I am looking for some help with the intermediate steps.

Thanks

Here it is set up for you in a "regular" viewing style. There should be a couple of
immediate steps** that you would take after seeing it like that. Write the result
down as a post on here so we can see your work.


\(\displaystyle \bigg(\dfrac{a}{t}\bigg)\bigg(\dfrac{\ t(d - t)\ }{ad}\bigg)\)




** dividing out/cancelling out like factors
 
Can I cancel out a to give:

[FONT=MathJax_Size3]([/FONT][FONT=MathJax_Math]1/[/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Size3])[/FONT][FONT=MathJax_Size3]([/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]d[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Main])/[/FONT][FONT=MathJax_Math]d[/FONT][FONT=MathJax_Size3])[/FONT]

then cancel out t, so:
[FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]d[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Main])/[/FONT][FONT=MathJax_Math]d[/FONT]


I think that I can't do that...?
 
Can I cancel out a to give:

[FONT=MathJax_Size3]([/FONT][FONT=MathJax_Math]1/[/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Size3])[/FONT][FONT=MathJax_Size3]([/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]d[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Main])/[/FONT][FONT=MathJax_Math]d[/FONT][FONT=MathJax_Size3])[/FONT]

then cancel out t, so:
[FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]d[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Main])/[/FONT][FONT=MathJax_Math]d[/FONT]


I think that I can't do that...?

Yes, both of those cancellations are legitimate.


(d - t)/d \(\displaystyle \ \ \)is good so far.


Look at it as \(\displaystyle \ \ \dfrac{d - t}{d}.\)


Split it up into: \(\displaystyle \ \ \dfrac{d}{d} \ - \ \dfrac{t}{d}\)


What can you do with that step?
 
Yes, both of those cancellations are legitimate.


(d - t)/d \(\displaystyle \ \ \)is good so far.


Look at it as \(\displaystyle \ \ \dfrac{d - t}{d}.\)


Split it up into: \(\displaystyle \ \ \dfrac{d}{d} \ - \ \dfrac{t}{d}\)


What can you do with that step?

When it is written like that, it is so obvious. d/d = 1, which gives the result I expect.

Thanks!
 
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