Question

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Answer 1

`(7x + 42)/(x^(2) + 13x +42) = (7(x+6))/((x + 6)(x + 7)) = (7)/(x + 7)`



`Answer C.) (7)/(x+7)`


`\textbf{Spymore}`

Answer 2

`\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ \cfrac{7x + 42}{x {}^(2) + 13x + 42 } }`

`\: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{\frac{7(x + 6)}{x {}^(2) + 13x + 42 \\ } }`

Note: To solve a problem like this, the first thing we must do is Extract the common factor of 7, then we have to know that the numbers that add up to 13 and multiply 42 is 6 and 7, then we must write the expression using the previous explanation which is the following:

`\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{( x + 6 ) (x+7)}`

Now with the above we must put it as a denominator, as follows:

`\: \: \: \: \: \: \: \: \: \: \bold{(7(x + 6))/((x + 6) + (x + 7) \\ ) }`

Finishing with the problem, the last thing we have to do is cancel
`\bold{x + 6}`

`\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{(7)/(x + 7 \\ ) }`

`\therefore` The result of the problem is :
`\bold{(7)/(x + 7 \\ ) }`