Question

The numerator of a fraction is 3 less than its denominator
If 2 is added to both the numerator and the denominator
then thesum of the new fraction and original fraction is
Find the original fraction.
20​

Answer 1

Answer:

$Let the fraction be = ( x - 3) \div x$

Let the fraction be =

$(x - 3) \div 3$

By the given condition, new fraction=

$(x - 3 + 2) \div (x + 2)$

$= (x - 1) \div(x - 2)$

$= (x - 3) \div 3 +( x - 1) \div (x + 2)$

$= 29 \div 20$

$20((x - 3)(x + 2) + x(x - 1) = 29 {x}^{2} + 2x)$

$= > 20(2 {x}^{2} - 2x - 6) = 29 {x}^{2} + 58x$

$= > 40 {x}^{2} - 40x - 120 - 29 {x}^{2} - 58x = 0$

$= > 11 {x}^{2} - 98x - 120 = 0$

$= > 11 {x}^{2} - 110x + 12x - 120 = 0$

$= > 11x(x - 10) + 12(x - 10) = 0$

$= > (x - 10)(11x + 12) = 0$

$= > x - 10 = 0 \\ = > x = 10$

or

$= > 11x + 12 = 0 \\ = > 11x = - 12 \\ = > x = - 12 \div 11$

rejected

hence the fraction will

be 7/10

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