Math Olympics Problem: Solving Equations with Fractions - Tips & Tricks

[Someone1348]

Homework Statement

I had this problem on the national math olympics of my country yesterday, I couldn't solve it... Knowing that the first statement is true, calculate the value of the second equation.

Homework Equations

\frac{a}{b+c+d}+\frac{b}{c+d+a}+\frac{c}{a+b+d}+\frac{d}{a+b+c}=1

Calculate the value of

\frac{a^2}{b+c+d}+\frac{b^2}{c+d+a}+\frac{c^2}{a+b+d}+\frac{d^2}{a+b+c}

The Attempt at a Solution

I lost a lot of time in this problem. I first tried to make one single, although huge, fraction of it, yet it didn't seem to simplify itself just to one value. Any better ways to approach this?

By the way, please excuse me if I posted this on the wrong forum, I just found this website and am still getting used to it. Also, since it isn't my homework or something I have to eventually give as homework, it doesn't matter if you show me directly the answer... I just posted it on this forum because it somewhat looked like the right one.

 

[Mentallic]

Caculate the following:

\frac{a+b+c+d}{a+b+c+d}\left(\frac{a}{b+c+d}+\frac{b}{a+c+d}+\frac{c}{a+b+d}+\frac{d}{a+b+c}\right)=1