B3. Calculate the value of the expression $\left(a^{2}-a b+b^{2}\right):\left(2 a^{2}-6 b\right)$, if $a-b=3$ and $\frac{2(a-b)}{3}-\frac{a+2 b}{9}=1$.
B3. From $a-b=3$ we express $a=b+3$ and substitute it into the equation $\frac{2(a-b)}{3}-\frac{a+2 b}{9}=1$, from which we get $b=2$ and thus $a=5$. We substitute the calculated values into the expression $\left(a^{2}-a b+b^{2}\right):\left(2 a^{2}-6 b\right)$ and get the result $\frac{1}{2}$.

Writing $a=b+3$ .1 point

Substituting the variable $a$ into the equation $\frac{2(a-b)}{3}-\frac{a+2 b}{9}=1$ .1 point

(Or correctly solving the system .......................................................................................................

For the calculated variable $b=2$ ....................................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_ce887fced8b2a2bf0894g-11.jpg?height=55&width=1641&top_left_y=612&top_left_x=276)

Substituting the values for $a$ and $b$ .......................................................................................................

Result: $\frac{1}{2}$ (the fraction must be simplified) ...............................................................