Basic Algebra Test

Algebra Level 4

Given that

ab+c+ba+c+ca+b=1, \frac{ \color{#D61F06}{a}}{\color{#3D99F6}{b}+\color{#EC7300}{c}} + \frac{\color{#3D99F6}{b}} {\color{#D61F06}{a}+\color{#EC7300}{c}} + \frac{ \color{#EC7300}{c}}{\color{#D61F06}{a}+\color{#3D99F6}{b}} = 1,

find the value of

a2b+c+b2a+c+c2a+b.\large \frac{ \color{#D61F06}{a}^2}{\color{#3D99F6}{b}+\color{#EC7300}{c}} + \frac{ \color{#3D99F6}{b}^2}{\color{#D61F06}{a}+\color{#EC7300}{c}} + \frac{ \color{#EC7300}{c}^2} { \color{#D61F06}{a}+\color{#3D99F6}{b}}.

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