hlo answer this and take 40 points the numerator of a fraction is 6 le

1.	hlo answer this and take 40 points the numerator of a fraction is 6 less than the denominator. if 3 is added to the numerator, the fraction is equal to 2\3,find the original fraction
Answer» GIVEN :– • The numerator of a fraction is 6 less than the DENOMINATOR. • If 3 is added to the numerator, the fraction is equal to ⅔ . TO FIND :– • ORIGINAL fraction = ? SOLUTION :– • Let the denominator 'x' . • So , Numerator = x - 6 ▪︎ ACCORDING to the QUESTION – $\\ \implies\sf \dfrac{(x - 6) + 3}{x + 3} = \dfrac{2}{3} \\$ $\\ \implies\sf \dfrac{x - 3}{x + 3} = \dfrac{2}{3} \\$ $\\ \implies\sf 3(x - 3)= 2(x + 3) \\$ $\\ \implies\sf 3x - 9= 2x + 6 \\$ $\\ \implies\sf 3x - 2x= 9+ 6 \\$ $\\ \implies\sf x= 9+ 6 \\$ $\\ \implies \large{ \boxed{\sf x=15 }}\\$ • HENCE – $\\ \implies \sf \: original \: \: fraction = \dfrac{15 - 6}{15} \\$ $\\ \implies \large{ \boxed{ \sf \: original \: \: fraction = \dfrac{9}{15}}} \\$