## simplification

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
twistedesoterix
Posts: 3
Joined: Tue Mar 04, 2014 7:35 am
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### simplification

So, I haven't had algebra in 2 years and I'm stuck. I need to simplify this whole mess. This is actually from my Enzyme Kinetics class but I'm stuck with the algebra...

v0={(Vmax*)/(Km+)}/{(Vmax*)/(Km(1+(/KI))+)}

I got as far as...
v0= {(Km(1+(/KI))+)} / (Km+)

After that, I don't know what to do. Any help would be much appreciated...

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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### Re: simplification

v0={(Vmax*)/(Km+)} / {(Vmax*)/(Km(1+(/KI))+)}

I got as far as...
v0= {(Km(1+(/KI))+)} / (Km+)

Before we proceed, are the above correctly converted below into "mathiness"?

. . . . .$v_0\, =\, \frac{ \left( \frac{V_{max}\, S}{K_m\, +\, S} \right) }{ \left( \frac{V_{max}\, S}{ K_m\, \left(1\, +\, \frac{I}{K_I}\right)\, +\, S } \right) }$

. . . . .$v_0\, =\, \frac{ K_m\, \left(1\, +\, \frac{I}{K_I}\right)\, +\, S }{ K_m\, +\, S }$

(If so, then you've done the first step correctly.) Thank you!

twistedesoterix
Posts: 3
Joined: Tue Mar 04, 2014 7:35 am
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### Re: simplification

Yes, that's correct! I'm new & I was typing that on my iPad. Thank you. What do I do after that? How can I further simplify this?

FWT
Posts: 153
Joined: Sat Feb 28, 2009 8:53 pm

### Re: simplification

Yes, that's correct! I'm new & I was typing that on my iPad. Thank you. What do I do after that? How can I further simplify this?
. . . . .$v_0\, =\, \frac{ K_m\, \left(1\, +\, \frac{I}{K_I}\right)\, +\, S }{ K_m\, +\, S }$

I think you can do out the fraction but that's about it.

$\frac{K_m\, +\, \frac{K_m I}{K_I}\, +\, S}{K_m\, +\, S}$

Nothing factors so nothing cancels. You could maybe rearrange but that probably won't be "simplifying":

$\frac{\left(K_m\, +\, S\right)\, + \frac{K_m I}{K_I}}{\left(K_m\, +\, S\right)}\, =\, 1\, +\, \left(\frac{\frac{K_m I}{K_I}}{K_m\, +\, S}\right)$

twistedesoterix
Posts: 3
Joined: Tue Mar 04, 2014 7:35 am
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### Re: simplification

Your last equation! That's what I needed to get to. Thank you so much! My book explained how to get the ratio and the last equation but didn't explain how to get there (since it's not a math class).

Thank you sooo much!!!