Mike:

(1) You have to understand something clearly. This is elementary stuff. If you slur over it it will haunt you forever. Write your equations carefully, noting that 4/3x IS NOT THE SAME AS (4/3)x. See below.

Treat 4/3x as 4/(3x), Solve

1/x = 4/3x + 1 = 4/(3x) +1

Sometimes it easier to multiply both sides by the x in the denominator. You get

1 = 4/3 + 1/x

1 - 4/3 = 1 / x

(3-4)/3 = 1/x

(-1)/3 = 1/x

x= - 3.

On the other hand IF YOU TAKE 4/3x as (4/3)x, then

1/x = (4/3)x + 1

1 = (4/3) x^{2} + x

3 = 4x^{2} + 3x

4x^{2} - 3x + 3 = 0

This is a quadratic equation in x. It has two roots, given by x = {3 (+ or -) sqrt[9 - 4(4)(3)]}/8. Perhaps at this time this is beyond what you are learning. Nonetheless, it is important enough to realize the difference between 4/(3x) and (4/3)x.

(2) 1/R=1/R1+1/R2 solve for R1.

One way to get rid of those pesky reciprocals is to find the LCM (least common multiple) of them (here RxR1XR2) and multiply throughout: You get

(R1)(R2) = (R)(R2) + (R)(R1)

Since you want to solve for R1, collect on one side all the terms in R!:

(R!) (R2 - R) = (R)(R2).

So

R1 = [(R)(R2)]/(R2 - R1). Done.

(3) a^2x+(a-1)=(a+1)x solve for x

Once again, Mike, you have a BIG HEADACHE! Look at a^2x. Tell me whether you mean by it, (a^2)x OR a^(2x). Your answer is pretty well going to depend on what you mean.

(a) Take a^2x as (a^2) x.

a^{2}x + (a-1) = (a+1) x

a^{2} x+ a - 1 = ax + x

x(a^{2} - a-1) = 1 - a

x = (1- a)/(a^{2} - a - 1) Done.

(b) Take a^2x as a^(2x)

a^{2x} + (a-1) = (a+1)x

This equation is definitely beyond you scope as of now. But you should STILL know how to write a^2x correctly.

Mike, please, learn carefully, what the symbols mean and how to write them correctly. Best.

Dattaprabhakar (Dr. G.)

William L.

Part of the answer is missing from the copy and past! I will update.

09/04/12