SOLUTION: (3^b)/(5)-(1)/(5)=(b)/(5) I need help solving the rational equation. could you do a step by step please??

Algebra ->  Rational-functions -> SOLUTION: (3^b)/(5)-(1)/(5)=(b)/(5) I need help solving the rational equation. could you do a step by step please??      Log On


   



Question 295568: (3^b)/(5)-(1)/(5)=(b)/(5) I need help solving the rational equation. could you do a step by step please??
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
You must have meant 3%2Ab not 3%5Eb

because there is no solution to 

%283%5Eb%29%2F5-1%2F5=b%2F5

and similar equations cannot be solved except 
by iterative methods, not by the mothods of 
ordinary algebra. 

So please learn that %223%5Eb%22 means 3%5Eb, not 3%2Ab

I will assume you meant:

%283%2Ab%29%2F5-1%2F5=b%2F5

Enclose every term in parentheses:

%28%283%2Ab%29%2F5%29-%281%2F5%29=%28b%2F5%29

The LCD is red%285%29, so write it as red%28%285%2F1%29%29
and multiply every term by that

  

Now cancel away the 5 denominators:



3%2Ab-1=b

Add 1 to both sides

3%2Ab=b%2B1

Add -b to both sides:

2%2Ab=1

Divide both sides by red%282%29

%282%2Ab%29%2Fred%282%29=1%2Fred%282%29

%28cross%282%29%2Ab%29%2Fred%28cross%282%29%29=1%2Fred%282%29

b=1%2F2

Edwin