Question

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

Answer 1

$\frac{7x+42}{x^2+13x+42}= \frac{7(x+6)}{x^2+7x+6x+42}= \frac{7(x+6)}{x(x+7)+6(x+7)}= \frac{7(x+6)}{(x+6)(x+7)}= \frac{7}{x+7}$

Answer 2

Answer:

The simplified expression is given by:

                $\dfrac{7}{x+7}$

Step-by-step explanation:

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:

                    $\dfrac{7}{x+7}$