What is the value of $\frac{a^2}{b+c} + \frac{b^2}{a+c} + \frac{c^2}{a+b}$ if $\frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b} = 1$? If $$\frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b} = 1$$ then find the values of $$\frac{a^2}{b+c} + \frac{b^2}{a+c} + \frac{c^2}{a+b}.$$ How can I solve it? Please help me. Thank you in advance.

HINT:
$$\dfrac{a^2}{b+c}+a=\dfrac{a(a+b+c)}{b+c}$$
$$\sum_{\text{cyc}}\left(\dfrac{a^2}{b+c}+a\right)=(a+b+c)\sum_{\text{cyc}}\dfrac a{b+c}$$
