finding solution to simultaneous equations I have three equations
$$ 
\begin{align*}
      c_1 & = \frac{a}{1+a+b} + \frac{a}{a+b}+\frac{a}{1+a}\\
   c_2 & = \frac{b}{1+a+b} + \frac{b}{a+b}+\frac{b}{1+b}\\
c_3 & = \frac{1}{1+a+b} + \frac{1}{1+a}+\frac{1}{1+b}\\
\end{align*}$$
where $c_1,c_2,c_3$ are known constant. 
I want to know if I can find $a$ and $b$ or not.. 
Thanks,

Before undertaking calculations which are guaranteed to be tedious, sometimes it helps to graph the equations involved. In this case if we turn these into equations in $x$ and $y$ by letting $x=a$ and $y=b$. Using the graphing site desmos.com and letting $c_1,\,c_2,\,c_3$ be 'sliders' we see that the places where the three graphs contain the same point cannot actually be solutions since they would lead to division by $0$.
For example, $a=x=-1$ and $b=y=0$ involve division by zero, as does $a=x=0$ and $b=y=-1$. We can get a solution $a=x=b=y=0$ but only for the case $c_1=c_2=0$ and $c_3=3$.
There are cases where a common intersection can be obtained but they require specific values of $c_1,\,c_2,\,c_3$. For example, if we let $c_1=c_2=c_3=\frac{4}{3}$ then $a=b=1$ is a solution.
So in general, no, one cannot solve for $a$ and $b$.
Here is the link to the Desmos graphs.
