Question

Assuming that $\frac{a}{b}<\frac{c}{d} < 1 $, arrange $\frac{b}{a}$, $\frac{d}{c}$, $\frac{bd}{ac}$, $\frac{b+d}{a+c}$, and $1$

score 149 · Answer 1 · 2015-12-31 10:57:07

149

Views

Assuming that $\frac{a}{b}<\frac{c}{d} < 1 $, arrange $\frac{b}{a}$, $\frac{d}{c}$, $\frac{bd}{ac}$, $\frac{b+d}{a+c}$, and $1$

Published on 31 Dec 2015 - 10:57

score 138 · Answer 2 · 2015-12-31 14:33:06

138

Views

How do we compare fraction without changing to a similar denominator?

Published on 31 Dec 2015 - 14:33

score 242 · Answer 3 · 2016-01-02 02:18:17

242

Views

Proving that $\frac{a}{b} = \frac{c}{d}$ if and only if $ad = bc$

Published on 02 Jan 2016 - 2:18

score 50 · Answer 4 · 2016-01-03 16:42:13

50

Views

Multiplication of algebraic fraction not giving desired result

Published on 03 Jan 2016 - 16:42

score 89 · Answer 5 · 2016-01-04 16:21:30

89

Views

Unit Fraction Addition

Published on 04 Jan 2016 - 16:21

score 49 · Answer 6 · 2026-03-30 06:29:11

49

Views

Find original cost based on fractional purchase

Published on 30 Mar 2026 - 6:29

score 1.9k · Answer 7 · 2016-01-06 12:31:08

1.9k

Views

Use the Cauchy-Schwarz Inequality to prove that $a^2+b^2+c^2 \ge ab+ac+bc $ for all positive $a,b,c$.

Published on 06 Jan 2016 - 12:31

score 116 · Answer 8 · 2026-03-12 15:45:54

116

Views

inequality with three variables and condition

Published on 12 Mar 2026 - 15:45

score 423 · Answer 9 · 2026-03-29 12:26:38

423

Views

How to properly set up partial fractions for repeated denominator factors

Published on 29 Mar 2026 - 12:26

score 148 · Answer 10 · 2026-03-30 06:29:53

148

Views

If the chance of an event was $1/128$ and increased by $20\%$, what is the new chance?

Published on 30 Mar 2026 - 6:29

score 241 · Answer 11 · 2026-03-31 09:45:02

241

Views

Prove that $\frac{1}{1+a_1+a_1a_2}+\frac{1}{1+a_2+a_2a_3}+\cdots+\frac{1}{1+a_{n-1}+a_{n-1}a_n}+\frac{1}{1+a_n+a_na_1}>1.$

Published on 31 Mar 2026 - 9:45

score 135 · Answer 12 · 2016-01-12 11:32:52

135

Views

How do I show that $-\frac{1}{e^x + 1} + 1 = \frac{e^x}{e^x + 1}$?

Published on 12 Jan 2016 - 11:32

score 128 · Answer 13 · 2026-03-31 12:45:27

128

Views

Laurent expansion of $\frac{1}{z^2}$

Published on 31 Mar 2026 - 12:45

score 133 · Answer 14 · 2016-01-13 08:37:17

133

Views

Solve fractions multiplication

Published on 13 Jan 2016 - 8:37

score 83 · Answer 15 · 2026-03-30 14:58:55

83

Views

Find the minimum of $\sum\limits_{cyc} {\sqrt{\frac a{2(b+c)}}}$ with $a,b,c \gt 0$

Published on 30 Mar 2026 - 14:58

List Question

Assuming that $\frac{a}{b}<\frac{c}{d} < 1 $, arrange $\frac{b}{a}$, $\frac{d}{c}$, $\frac{bd}{ac}$, $\frac{b+d}{a+c}$, and $1$

How do we compare fraction without changing to a similar denominator?

Proving that $\frac{a}{b} = \frac{c}{d}$ if and only if $ad = bc$

Multiplication of algebraic fraction not giving desired result

Unit Fraction Addition

Find original cost based on fractional purchase

Use the Cauchy-Schwarz Inequality to prove that $a^2+b^2+c^2 \ge ab+ac+bc $ for all positive $a,b,c$.

inequality with three variables and condition

How to properly set up partial fractions for repeated denominator factors

If the chance of an event was $1/128$ and increased by $20\%$, what is the new chance?

Prove that $\frac{1}{1+a_1+a_1a_2}+\frac{1}{1+a_2+a_2a_3}+\cdots+\frac{1}{1+a_{n-1}+a_{n-1}a_n}+\frac{1}{1+a_n+a_na_1}>1.$

How do I show that $-\frac{1}{e^x + 1} + 1 = \frac{e^x}{e^x + 1}$?

Laurent expansion of $\frac{1}{z^2}$

Solve fractions multiplication

Find the minimum of $\sum\limits_{cyc} {\sqrt{\frac a{2(b+c)}}}$ with $a,b,c \gt 0$

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