How does this numerators and denominators relate with the fraction? Suppose if we have two fraction

polivijuye

polivijuye

Answered question

2022-06-22

How does this numerators and denominators relate with the fraction?
Suppose if we have two fractions a b and c d then how are their values related with the fraction a + c b + d ?
I have observed this inequality: a b a + c b + d c d
Does this hold true a , b , c , d N ? Is there any proof?
I am sorry if this question is too basic, but I want help regarding this.

Answer & Explanation

Dustin Durham

Dustin Durham

Beginner2022-06-23Added 31 answers

HINT:
a + c b + d a b = b c a d b ( b + d ) = c d a b b 2 d ( b + d )
This will be > 0 if d ( b + d ) > 0 and c d a b > 0
lobht98

lobht98

Beginner2022-06-24Added 6 answers

we have
a + c b + d c d
if
c d a + c b + d = b c a d d ( b + d ) > 0
and this is true since
a b < c d
if
a d < b c
further we have
a + c b + d a b = b c a d b ( b + d )

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