the denominator of a rational number is greater than its numerator by

1.	the denominator of a rational number is greater than its numerator by 14.if the numerator and denominator are both increased by 5 the new number obtained is 11/18 find the original rational number
Answer» Step-by-step EXPLANATION: Lets take the numerator as x then denominator will BECOME (x+14) . If the numerator and denominator is increased by 5 then the NEW number is 11/18 the original rational number. New number is (x+5)/(x+19). $\frac{(x + 5)}{(x + 19)} = \frac{11}{18} \frac{x}{(x + 14)} = >$ $18(x + 14)(x + 5)= 11x(x + 19)= >$ $18( {x}^{2} + 14x + 5x + 70) = 11 {x}^{2} +$ $209x = > 18 {x}^{2} + 342x + 1260 =$ $11 {x}^{2} + 209x = > 18 {x}^{2} - 11 {x}^{2} +$ $342x - 209x + 1260 = 0 = > 7{x}^{2} +$ $133x + 1260 = 0 = > {x}^{2} + 19x +$ $180 = 0$ Determinant is NEGATIVE so no value of x can SATISFY the above conditions so it is not possible. Hope it helps you.