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formula simplification
- Thread starter dennyloi
- Start date
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:
then cancel out t, so:
[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!