The denominator of a fraction is 3 more than its
numerator. The sum of the fraction and its reciprocal
is 2 into 9/10. Find the fraction.
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Let the dfraction is
y
x
Then, according to given question
y=x+3.......(1)
Again,
y
x
+
x
y
=2
10
9
xy
x
2
+y
2
=
10
29
10x
2
+10y
2
=29xy.......(2)
Put the value of y in equation (2).
10x
2
+10(x+3)
2
=29x(x+3)
⇒10x
2
+10(x
2
+9+6x)=29x
2
+87x
⇒10x
2
+10x
2
+90+60x=29x
2
+87x
⇒20x
2
−29x
2
+60x−87x+90=0
⇒−9x
2
−27x+90=0
⇒−9(x
2
+3x−10)=0
⇒x
2
+3x−10=0
⇒(x+5)(x−2)=0byfactorize
⇒x+5=0x−2=0
⇒x=−5x=2
Put x=2 In equation (1)
y=2+3=5
fraction
y
x
=
5
2
ans.
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