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

Question

asked May 10, 2018 132k views

2 Answers

Bhavesh Dhaduk · Answer 1 · 2018-05-16T08:40:15+0000

The simplified expression is given by:

(7)/(x+7)

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)