Issues solving for variables

[solidusraven]

Issues solving for variables (pictures attached)

I basically have issues solving for variables when they are above and below the denominator. Here are a few examples of what I am referring to. Any help would be appreciated!<br>I would say I am having problems with most of them specially 17. Any help, examples, advise on what to work on or references would be appreciated.

 

[soroban]

Hello, solidusraven!

I basically have issues solving for variables when they are above and below the denominator.

. . \(\displaystyle 4.\;\;C \:=\:\dfrac{1}{C_1} + \dfrac{1}{C_2} \quad\text{ Solve for }R_2\)

Multiply through by the LCD, \(\displaystyle C_1C_2\)

. . . . . . . . . \(\displaystyle C_1C_2(C) \;=\;C_1C_2\left(\dfrac{1}{C_1}\right) + C_1C_2\left(\dfrac{1}{C_2}\right)\)

. . . . . . . . . . .\(\displaystyle C_1C_2C \;=\;C_2 + C_1\)

. . . . . . .\(\displaystyle C_1C_2C - C_2 \;=\;C_1\)


Factor: .\(\displaystyle (C_1C - 1)C_2 \;=\;C_1\)

. . . . . . . . . . . . . .\(\displaystyle C_2 \;=\;\dfrac{C_1}{C_1C - 1}\)

\(\displaystyle 17.\;\;R_o \:=\:\dfrac{R_1R_2}{R_1 + R_2}\quad\text{ Solve for }R_2\)

Multiply by \(\displaystyle (R_1+R_2)\)

. . . . . . .\(\displaystyle (R_1+R_2)R_o \;=\;(R_1+R_2)\left(\dfrac{R_1R_2}{R_1+R_2}\right) \)

. . . . . . .\(\displaystyle (R_1+R_2)R_o \;=\;R_1R_2\)

. . . . . .\(\displaystyle R_1R_o + R_2R_o \;=\;R_1R_2\)

. . . . . .\(\displaystyle R_2R_o - R_1R_2 \;=\;-R_1R_o\)


Factor: .\(\displaystyle (R_o - R_1)R_2 \;=\;-R_1R_o \)

. . . . . . . . . . . . . .\(\displaystyle R_2 \;=\;\dfrac{-R_1R_o}{R_o - R_1}\)


Multiply by \(\displaystyle \frac{-1}{-1}:\quad R_2 \;=\;\dfrac{R_1R_o}{R_1-R_o} \)

 

[tkhunny]

With that large a list, you seem to be saying you have not ever attended class?

If you have been attending class, I defintely blame your book or your instructor - whichever told you that these are more difficult than others you have solved successfully. The fundamental principles are EXCACTLY the same as less complicatred looking problems.

How do you solve this for x? \(\displaystyle 5 = \frac{1}{x}\)

1) Promise that x is NOT zero, and then multiply by x.

5x = 1

2) There, no more ugly denomninator and it's a simply division problem.

This is ALL you should be doing. It does NOT matter how scary-looking it is or may be.

How do you solve this for a very complicated expression for the only variable? \(\displaystyle 12 = \frac{GettysburgAddress}{1+GettysburgAddress}\)

1) Promise that 1 + GettysburgAddress is NOT zero (or Gettysburg Address is NOT -1) and then multiply by 1+GettysburgAddress.

12*(1+GettysburgAddress) = GettysburgAddress

2) There, no more ugly denominator and it's a relatively simply exercise in multiplication and collection.

Okay, with that, you show us how to do #17 and we'll happily tell you if you wander off.

Or, you can wait for someone else to do it for you and we'll never know if you learned anything.

Note: Never EVER multiply by ANYTHING until AFTER you KNOW it's not zero. EVER! (Unless you're willing to accept the possible consequences.)

 

[solidusraven]

Hello, solidusraven!


Multiply through by the LCD, \(\displaystyle C_1C_2\)

. . . . . . . . . \(\displaystyle C_1C_2(C) \;=\;C_1C_2\left(\dfrac{1}{C_1}\right) + C_1C_2\left(\dfrac{1}{C_2}\right)\)

. . . . . . . . . . .\(\displaystyle C_1C_2C \;=\;C_2 + C_1\)

. . . . . . .\(\displaystyle C_1C_2C - C_2 \;=\;C_1\)


Factor: .\(\displaystyle (C_1C - 1)C_2 \;=\;C_1\)

. . . . . . . . . . . . . .\(\displaystyle C_2 \;=\;\dfrac{C_1}{C_1C - 1}\)




Multiply by \(\displaystyle (R_1+R_2)\)

. . . . . . .\(\displaystyle (R_1+R_2)R_o \;=\;(R_1+R_2)\left(\dfrac{R_1R_2}{R_1+R_2}\right) \)

. . . . . . .\(\displaystyle (R_1+R_2)R_o \;=\;R_1R_2\)

. . . . . .\(\displaystyle R_1R_o + R_2R_o \;=\;R_1R_2\)

. . . . . .\(\displaystyle R_2R_o - R_1R_2 \;=\;-R_1R_o\)


Factor: .\(\displaystyle (R_o - R_1)R_2 \;=\;-R_1R_o \)

. . . . . . . . . . . . . .\(\displaystyle R_2 \;=\;\dfrac{-R_1R_o}{R_o - R_1}\)


Multiply by \(\displaystyle \frac{-1}{-1}:\quad R_2 \;=\;\dfrac{R_1R_o}{R_1-R_o} \)

I think that is where I got stuck on this one. I got stuck and didn't factor out those numbers. Thanks!

 

[solidusraven]

#17: same as a = bc / (b + c) ; solve for c

Step#1: a(b + c) = bc ; ab + ac = bc

Step#2: bc - ac = ab

Can you finish it?

This helped me simplify everything thanks!

 

[solidusraven]

With that large a list, you seem to be saying you have not ever attended class?

If you have been attending class, I defintely blame your book or your instructor - whichever told you that these are more difficult than others you have solved successfully. The fundamental principles are EXCACTLY the same as less complicatred looking problems.

How do you solve this for x? \(\displaystyle 5 = \frac{1}{x}\)

1) Promise that x is NOT zero, and then multiply by x.

5x = 1

2) There, no more ugly denomninator and it's a simply division problem.

This is ALL you should be doing. It does NOT matter how scary-looking it is or may be.

How do you solve this for a very complicated expression for the only variable? \(\displaystyle 12 = \frac{GettysburgAddress}{1+GettysburgAddress}\)

1) Promise that 1 + GettysburgAddress is NOT zero (or Gettysburg Address is NOT -1) and then multiply by 1+GettysburgAddress.

12*(1+GettysburgAddress) = GettysburgAddress

2) There, no more ugly denominator and it's a relatively simply exercise in multiplication and collection.

Okay, with that, you show us how to do #17 and we'll happily tell you if you wander off.

Or, you can wait for someone else to do it for you and we'll never know if you learned anything.

Note: Never EVER multiply by ANYTHING until AFTER you KNOW it's not zero. EVER! (Unless you're willing to accept the possible consequences.)

I was giving examples of the problems I was struggling. I completed them all of my own except the last 3. I never attended any of my classes "rolls eyes" lol. I took your advice on that one, seems simplistic and helpful!