Question 675336
The denominator of a certain fraction is three times the numerator. If 2 is added to the numerator and subtracted from the denominator, the result equals 3/5.

let {{{x}}} be denominator

given:

the denominator of a certain fraction is three times the numerator:
the denominator is  {{{3x}}}

so, fraction is:{{{x/3x}}}

If {{{2}}} is added to the numerator and subtracted from the denominator, the result equals {{{3/5}}}.

so, we have:

{{{(x+2)/(3x-2)=3/5}}}....solve for {{{x}}}


{{{(x+2)/(3x-2)=3/5}}}....cross multiply


{{{(x+2)*5=3(3x-2)}}}


{{{5x+10=9x-6}}}


{{{10+6=9x-5x}}}


{{{16=4x}}}


{{{x=16/4}}}


{{{x=4}}}


the original fraction is:


{{{x/3x}}}.........plug in {{{x}}}


{{{4/(3*4)}}}


{{{cross(4)1/(3*cross(4))}}}


{{{highlight(1/3)}}}