Question

The denominator of a fraction is 2 more than its numerator. The sum of the fraction and its reciprocal is 10/3. What is the fraction?

Answer 1

Step-by-step explanation:

let numerator be x

so, denominator = x+2

fraction = x/(x+2)

reciprocal = (x+2)/x

According. to question:

x/(x+2) + (x+2)/x = 10/3

taking lcm in LHS we get:

((x×x) + (x+2)× (x+2))/ x×(x+2)

(x^2+x^2+2x+4)/x^2+2x

(2x^2+2x+4)/ x^2+2x

equating both sides we get :

(2x^2+2x4)/x^2+2x =10/3

cross multiplying we get:

3 × (2x^2+2x+4) = 10 × (x^2 +2x)

6x^2 +6x +12 = 10x^2 +20x

transposing 10x^2 and 20x to LHS we get :

6x^2-10x^2 +6x -20x +12 =0

-4x^2 -12x +12 =0

taking -4 as common transposing it to RHS we get:

x^2+3x-4 =0

splitting the middle term we get :

x^2 +4x -x -4=0

x (x+4) - (x+4) =0

(x+4) (x-1) =0

x=-4 and x=1

but it is a fraction so, x=1 is relevant result

numerator =1

denominator =x+2= 1+2 =3

fraction =1/3