Question

The denominator of a fraction ia one more than teice the numerator. The sum of the fraction of its reciprocal is 58/21 find the fracyion

Answer 1

Answer:

Step-by-step explanation:

Let x be the numerator and y be the denominator.

Then fraction will be x/ y.

As given in the question,

y=2x+1.

Fraction=x/y= x/2x+1.

x/y + y/x = 58/21.

(x^2+y^2)/xy = 58/21.

21(x^2+y^2)=58(xy).

21(x^2+(2x+1)^2=58(x(2x+1)).

21(x^2+4x^2+1+4x)=58(2x^2+x).

21(5x^2+4x+1)=116x^2+58x.

105x^2+84x+21= 116x^2+58x.

116x^2-105x^2+58x-84x-21=0.

11x^2 - 26x -21 =0.

11x^2 -33x+7x-21=0.

11x(x-3)+7(x-3)=0.

(11x+7)(x-3)=0.

x-3=0.

x=3.

So Fraction= x/y where y= 2x+1.

x=3, y= 2x+1=2×3+1=7.

So the fraction is 3/7.

Hope it helps...