SOLUTION: i'm trying to show a=b or a=1/b without plugging in the values for a. this is the equation a+1/a=b+1/b i have tried multiplying both sides by ab i tried the quadratic equ

Algebra ->  Expressions-with-variables -> SOLUTION: i'm trying to show a=b or a=1/b without plugging in the values for a. this is the equation a+1/a=b+1/b i have tried multiplying both sides by ab i tried the quadratic equ      Log On


   

Question 445209: i'm trying to show a=b or a=1/b without plugging in the values for a.
this is the equation
a+1/a=b+1/b
i have tried multiplying both sides by ab
i tried the quadratic equation but that didn't work very well cause i couldn't get the square root out
i just need a step by step explanation of how to get there cause its driving me crazy and i think i'm just missing something simple
please remember. i know how to substitute. i'm basically proving a= b,1/b
which is why i tried making it a quadratic because i knew there were 2 answers
thank you very much
i hope you can help
Found 2 solutions by mananth, AnlytcPhil:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
a+(1/a)= b+(1/b)
%28a%5E2%2B1%29%2Fa=+%28b%2A2%2B1%29%2Fb
multiply by ab
b%28a%5E2%2B1%29=a%28b%5E2%2B1%29
ba%5E2%2Bb=ab%5E2%2Ba
ba%5E2-ab%5E2=a-b
ab(a-b)=(a-b)
/(a-b)
ab=1
a=1/b

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
a + 1/a = b + 1/b

Clear of fractions by multiplying through by ab

a²b + b = ab² + a

Get 0 on the right:

a²b + b - ab² - a = 0

Rearrange the terms:

a²b - ab² - a + b = 0

Factor by grouping:

ab(a - b) - (a - b) = 0

(a - b)(ab - 1) = 0

Us the zero factor principle:

a - b = 0;   ab - 1 = 0

    a = b;       ab = 1
     
                  a = 1/b

Edwin