Abstract Inequalities

**GrigOrig99** · November 2nd 2012, 10:25 AM

Can anyone help me confirm if I've solved this correctly?

Many thanks.

Q. If a, b, c, d are positive numbers & $\frac{a}{b}>\frac{c}{d}$ , prove that $\frac{a+c}{b+d}>\frac{c}{d}$ .

Attempt: 1st: if $\frac{a}{b}>\frac{c}{d}$
if $ad>bc$ ...true

2nd: if $\frac{a+c}{b+d}>\frac{c}{d}$
if $ad+cd>bc+cd$
if $ad>bc$ ...true

**Plato** · November 2nd 2012, 10:51 AM

Originally Posted by GrigOrig99

Can anyone help me confirm if I've solved this correc

Q. If a, b, c, d are positive numbers & $\frac{a}{b}>\frac{c}{d}$ , prove that $\frac{a+c}{b+d}>\frac{c}{d}$ .

From the given
$\begin{align*}ad &>bc\\ ad+cd &> bc+cd\\(a+c)d &>(b+d)c\\ \frac{a+c}{b+d}&>\frac{c}{d} \end{align*}$ .

**GrigOrig99** · November 2nd 2012, 11:23 AM

Great. Thank you.

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