Question

the denominator of a fraction is 3 more than the numerator. if both numerator and denominator are increased by 1, the resulting fraction is( 3)/(4.) find the fraction

Answer 1

`(8)/(11)`

Explanation:

let x be the numerator of the fraction then denominator is x + 3, so

`(x)/(x+3)` ← represents the original fraction

increasing the numerator and denominator by 1

=
`(x+1)/(x+3+1)` =
`(x+1)/(x+4)`

equating to
`(3)/(4)`

`(x+1)/(x+4)` =
`(3)/(4)` ( cross- multiply )

4(x + 1) = 3(x + 4) ← distribute parenthesis

4x + 4 = 3x + 12 ( subtract 3x from both sides )

x + 4 = 12 ( subtract 4 from both sides )

x = 8

and x + 3 = 8 + 3 = 11

the original fraction is therefore
`(8)/(11)`