$$( \frac { 6 } { 9 } ) ^ { 2 } + ( \frac { 3 } { 9 } ) ^ { 2 } + 2 \times \frac { 6 } { 9 } \times \frac { 3 } { 9 }$$
$1$
$$\left(\frac{2}{3}\right)^{2}+\left(\frac{3}{9}\right)^{2}+2\times \frac{6}{9}\times \frac{3}{9}$$
$$\frac{4}{9}+\left(\frac{3}{9}\right)^{2}+2\times \frac{6}{9}\times \frac{3}{9}$$
$$\frac{4}{9}+\left(\frac{1}{3}\right)^{2}+2\times \frac{6}{9}\times \frac{3}{9}$$
$$\frac{4}{9}+\frac{1}{9}+2\times \frac{6}{9}\times \frac{3}{9}$$
$$\frac{5}{9}+2\times \frac{6}{9}\times \frac{3}{9}$$
$$\frac{5}{9}+2\times \frac{2}{3}\times \frac{3}{9}$$
$$\frac{5}{9}+\frac{4}{3}\times \frac{3}{9}$$
$$\frac{5}{9}+\frac{4}{3}\times \frac{1}{3}$$
$$\frac{5}{9}+\frac{4}{9}$$
$$1$$
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