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zloy xaker [14]
3 years ago
9

Simplify (7x+42)/(x^2+13x+42)

Mathematics
2 answers:
Colt1911 [192]3 years ago
7 0
\frac{7x+42}{x^2+13x+42}=  \frac{7(x+6)}{x^2+7x+6x+42}=   \frac{7(x+6)}{x(x+7)+6(x+7)}=  \frac{7(x+6)}{(x+6)(x+7)}=  \frac{7}{x+7}
grandymaker [24]3 years ago
4 0
<h2>Answer:</h2>

The simplified expression is given by:

                \dfrac{7}{x+7}

<h2>Step-by-step explanation:</h2>

We are asked to simplify the expression which is given in terms of variable x as:

             =\dfrac{7x+42}{x^2+13x+42}

The given expression is a rational expression as it is a polynomial expression in the denominator as well as in the numerator.

Now we know that:

7x+42=7(x+6)

and

x^2+13x+42=x^2+7x+6x+42\\\\\\i.e.\\\\\\x^2+13x+42=x(x+7)+6(x+7)\\\\\\i.e.\\\\\\x^2+13x+42=(x+7)(x+6)

Hence, we get:

\dfrac{7x+42}{x^2+13x+42}=\dfrac{7(x+6)}{(x+6)(x+7)}\\\\\\i.e.\\\\\\\dfrac{7x+42}{x^2+13x+42}=\dfrac{7}{x+7}

            Hence, the simplified expression is:

                    \dfrac{7}{x+7}

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