Question

The volume of a fraction is 2 less than the denominator. If the denominator is multiplied by 2 and the denominator is multiplied by 3, the fraction becomes 2/9. Fraction?​

Answer 1

Answer:

$Let the numerator of the fraction be x. </p><p></p><p></p><p>Then Denominator=2x+1</p><p>Fraction =2x+1x</p><p>Reciprocal of the fraction =x2x+1</p><p>It is given that the sum fo the fraction and its reciprocal is 22116</p><p>∴2x+1x+x2x+1=221 \frac{?1}{?6} </p><p></p><p></p><p>⇒x(2x+1)x2+(2x+1)2=2158⇒2x2+x5x2+4x+1=2158</p><p></p><p></p><p>⇒21(5x2+4x+1)=58(2x2+x)⇒105x2+84x+21=116x2+58x</p><p></p><p></p><p>⇒11x2−26x−21=0⇒11x</p><p></p><p>$