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

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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