Answer:
2( w + 6)
Explanation:
We have to put some expressions into the blank such that rational expression on the light simplifies to equal the rational function on the left.
Now let us make a guess and say that the expression to write in the blank is 2 (w +6). Putting this guess into the blank gives
[tex]\frac{2(w+6)}{(w+6)(w+7)}[/tex]
the term w + 6 cancels from both the numerator and the denominator to give
[tex]\frac{2}{w+7}[/tex]
which is exactly the expression we find on the left-hand side of our original equality!
This tells us that our guess was correct and the expression to be filled into the blank is 2( w+ 6).
