Question 389491

The denominator of the fraction is 2 more than the numerator. If 1 is subtracted from both numerator and denominator, the resulting fraction has a value of 1/2. Find the original fraction. (Need a complete solution for this. Thanks)


let the numerator be {{{x}}} and denominator {{{y}}}


given: the denominator of the fraction is {{{2}}} more than the numerator ; so, {{{y=x+2}}}

the fraction is
{{{x/(x+2)}}}

If {{{1}}} is subtracted from both numerator and denominator, the resulting fraction has a value of {{{1/2}}}, so we will have

{{{(x-1)/(x+2-1)=1/2}}}

{{{(x-1)/(x+1)=1/2}}}...cross multiply

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

{{{2x-2=1x+1}}}..........solve for {{{x}}}

{{{2x- x = 2+1}}}

{{{x = 3}}}..........the numerator 

{{{y=x+2}}}
{{{y=3+2}}}
{{{y=5}}}..........the denominator

so, fraction is  {{{3/5}}}

check:

If {{{1}}} is subtracted from both numerator and denominator, the resulting fraction has a value of {{{1/2}}}, so we will have

 {{{(3-1)/(5-1)=2/4=1/2}}}