aluate $$ \frac{(2 g-f)(f+g)^{2}}{g f+7} $$ $$ f=1 $$ and $$ g=2 $$

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UpStudy AI · Accepted Answer

1. Substitute $$ f = 1 $$ and $$ g = 2 $$ into the expression:
   $$
   \frac{(2g-f)(f+g)^2}{gf+7} = \frac{(2 \cdot 2 - 1)(1+2)^2}{1 \cdot 2 + 7}
   $$

2. Simplify the numerator:
   $$
   2 \cdot 2 - 1 = 4 - 1 = 3
   $$
   $$
   1 + 2 = 3 \quad \text{so} \quad (1+2)^2 = 3^2 = 9
   $$
   Thus, the numerator is:
   $$
   3 \cdot 9 = 27
   $$

3. Simplify the denominator:
   $$
   1 \cdot 2 + 7 = 2 + 7 = 9
   $$

4. Combine the results:
   $$
   \frac{27}{9} = 3
   $$

The final answer is $$ 3 $$.
The final answer is 3.

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