The denominator of a fraction is one less than twice the numerator. If the sum of the fraction and it's reciprocal is 34/15 find the fraction.
plz give precise answer!
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Answer:
3/7
Step-by-step explanation:
Let the fraction 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.
THERE YOU GO MATE!!!!!!!!!! HOPE IT HELPS YOU
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