# Finding a value of an expression (fraction)

• February 27th 2011, 05:51 PM
lanierms
Finding a value of an expression (fraction)
$a, b, c$ are positive real numbers.

If they satisfy the equations:

$(\frac{b}{a}+\frac{a}{b})(\frac{1}{a}+\frac{1}{b}+ \frac{1}{c})=\frac{70}{a+b+c}$

$(\frac{c}{b}+\frac{b}{c})(\frac{1}{a}+\frac{1}{b}+ \frac{1}{c})=\frac{90}{a+b+c}$

$(\frac{a}{c}+\frac{c}{a})(\frac{1}{a}+\frac{1}{b}+ \frac{1}{c})=\frac{110}{a+b+c}$

Find the value of

$(a+b+c)(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})$.