Question 325319
if the numerator is increased by 1 and the denominator is reduced by 1,the value of the fraction becomes 1.find the original
<pre><b>
Let N = the numerator
Let D = the denominator
Then {{{N/D}}} = the fraction


{{{system(N/D=2/3,(N+1)/(D-1)=1)}}}

{{{system(3N=2D,N+1=D-1)}}}

{{{system(3N=2D,N=D-2)}}}

Use substitution, replace N in the first by D-2 from the second

{{{3N=2D}}}

{{{3(D-2)=2D}}}

{{{3D-6=2D}}}

{{{D=6}}}

Substitute that in

{{{N=D-2)}}}

{{{N=6-2)}}}

{{{N=4}}}

So the fraction is {{{4/6}}}

Checking:

Adding one to the numerator and subtracting one from the
denominator gives {{{(4+1)/(6-1)=5/5=1}}}

Edwin</pre>