Question

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

Answer 1

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

Answer 2

The simplified expression is given by:

`(7)/(x+7)`

Explanation:

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

`=(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:

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

Hence, the simplified expression is:

`(7)/(x+7)`