# Abstract Inequalities

• November 2nd 2012, 10:25 AM
GrigOrig99
Abstract Inequalities
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
• November 2nd 2012, 10:51 AM
Plato
Re: Abstract Inequalities
Quote:

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*}.
• November 2nd 2012, 11:23 AM
GrigOrig99
Re: Abstract Inequalities
Great. Thank you.