How do I simplify an algebraic equation with respect to a specific variable?

Question

I have the following equation -- which is all in terms of d:

{{{{acc == {(d + d (-1 + 1/fpr) (-1 + 1/precision))/(
  d + d (-1 + 1/precision) + d (-1 + 1/fpr) (-1 + 1/precision) + 
   d (-1 + 1/tpr))}}}}}

and I want it to now express this in terms of d. I thought I could use

 Solve[acc, {d}, MaxExtraConditions -> Automatic ]

but I get an error message. Now I could do this by hand, but I'm new to Mathematica. I have read the documentation, but I am unsure what I have missed or got wrong.

You can't use curly brackets like they are parenthesis. They are used to build lists. — Sjoerd C. de Vries, Mar 23 '15 at 16:17

m_goldberg · Answer 1 · 2015-03-23T15:56:27.323

2

First off: you have a lot of unnecessary bracket pairs. Your equation should be written

acc == 
  (d + d (-1 + 1/fpr) (-1 + 1/precision))/
    (d + d (-1 + 1/precision) + d (-1 + 1/fpr) (-1 + 1/precision) + 
      d (-1 + 1/tpr))

Second, since d can be eliminated from your equation, you can't get a solution in terms of d.

Eliminate[
 acc == 
   (d + d (-1 + 1/fpr) (-1 + 1/precision))/
     (d + d (-1 + 1/precision) + d (-1 + 1/fpr) (-1 + 1/precision) + 
       d (-1 + 1/tpr)),
   d] // Simplify

fpr precision + tpr - precision tpr != 0 && 
acc == ((1 - fpr - precision + 2 fpr precision) tpr)/
         (fpr precision + tpr - precision tpr)

edited Mar 23 '15 at 15:56

answered Mar 23 '15 at 15:36

m_goldberg

107,779
16
103
257

Hello! Thanks for help. The unnecessary bracket pairs are what are generated by Mathematica and I have no idea why it does this... so that Solve[tpr == d/(c + d), c generates {{c -> (d - d tpr)/tpr}} - it's not me putting them in! How do I stop these being generated? When I use Eliminate(acc,d) I get an error saying "acc is not a well-formed equation" but if I manually delete all the {{{}}} then the elimination works as @m_goldberg have suggested. – Nick Ryman-Tubb Mar 23 '15 at 16:40
@NickRyman-Tubb This explanation should be helpful. – Karsten7 Mar 23 '15 at 17:22

score 0 · Answer 2 · answered Mar 23 '15 at 16:02

0

First, you use a wrong syntax for Solve. It should be something like

eq = acc == whatever the right hand side is;
Solve[eq, d]

Second, as m_goldberg has pointed out, your equation just can't be solved in terms of d! You must have done something wrong in your hand calculation.

answered Mar 23 '15 at 16:02

Taiki

5,259
26
34

Hello - yes I seem to have eliminated d! Still I cannot work out why my solve seems to generate lots of {{}}! I've only be a user for 15 mins! – Nick Ryman-Tubb Mar 23 '15 at 16:55

How do I simplify an algebraic equation with respect to a specific variable?

2 Answers2