Question

The denominator of a fraction is two more than the numerator. If both numerator and denominator are increased by nine, the simplified result is 1415

. Find the original fraction. (Do NOT simplify.)

Answer 1

original fraction is
`(19)/(21)`

Explanation:

let x be the numerator , then x + 2 is the denominator , then original fraction is

`(x)/(x+2)`

adding 9 to numerator and denominator

`(x+9)/(x+2+9)` =
`(x+9)/(x+11)`

equate this fraction to
`(14)/(15)`

`(x+9)/(x+11)` =
`(14)/(15)` ( cross- multiply )

15(x + 9) = 14(x + 11) ← distribute parenthesis on both sides

15x + 135 = 14x + 154 ( subtract 14x from both sides )

x + 135 = 154 ( subtract 135 from both sides )

x = 19

then original fraction is
`(19)/(21)`