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in a rational no. twice the numerator is 2 more than the denominator. if 3 is added to each, the numerator or the denominator, the new fraction is 2/3. find the original no.



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luana
[tex]\frac{x}{y}- rational\ number\\\\2x-2=y\\\\ \frac{x}{2x-2}- rational \ number\\\\ \frac{x+3}{2x-2+3}=\frac{2}{3}\\\\Cross\ multiplication\\\\3(x+3)=2(2x-2+3)\\\\3x+9=2(2x+1)\\\\3x+9=4x+2\\\\3x-4x=2-9\\\\-x=-7\ |*(-1)\\\\x=7\\\\Original \ number\ is\ \frac{7}{2*7-2}=\frac{7}{12}[/tex]

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