6.1 Areas Between Curves/10

${\begin{aligned}&\color {red}\mathbf {y=1+{\sqrt {x}}} &\color {royalblue}\mathbf {y={\frac {3+x}{3}}} \\\\\end{aligned}}$

${\begin{aligned}&1+{\sqrt {x}}={\frac {3+x}{3}}\\[2ex]&=1+{\sqrt {x}}-{\frac {3+x}{3}}=0\\&={\frac {3+3{\sqrt {x}}}{3}}-{\frac {3+x}{3}}=0\\&=3+3{\sqrt {x}}-3+x=0\\&=3{\sqrt {x}}+x=0\\&=3{\sqrt {x}}=-x\\&=9x=x^{2}\\&=9x-x^{2}=0\\&=x(9-x)=0\\&=x=0,9\end{aligned}}$