Question

1. $\frac{g - 2}{\frac{g^{2}-10g + 21}{g - 2}}div\frac{g^{2}-9g + 18}{g - 2}$

Explanation:

Step1: Rewrite division as multiplication

Dividing by a fraction is the same as multiplying by its reciprocal. So $\frac{g - 2}{g^{2}-10g + 21}\div\frac{g - 2}{g^{2}-9g+18}$ becomes $\frac{g - 2}{g^{2}-10g + 21}\times\frac{g^{2}-9g + 18}{g - 2}$.

Step2: Factor the quadratic expressions

Factor $g^{2}-10g + 21=(g - 3)(g - 7)$ and $g^{2}-9g + 18=(g - 3)(g - 6)$. So the expression is $\frac{g - 2}{(g - 3)(g - 7)}\times\frac{(g - 3)(g - 6)}{g - 2}$.

Step3: Cancel out common factors

Cancel out the common factors $(g - 2)$ and $(g - 3)$. We get $\frac{g - 6}{g - 7}$.

Answer:

$\frac{g - 6}{g - 7}$