How do you find the excluded value and simplify (x^2-13x+42)/(x+7)?

2 Answers
May 12, 2018

"excluded value "=-7

Explanation:

The denominator of the rational expression cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.

"solve "x+7=0rArrx=-7larrcolor(red)"excluded value"

"to simplify factorise the numerator and cancel any "
"common factors"

"the factors of + 42 which sum to - 13 are - 6 and - 7"

rArrx^2-13x+42=(x-6)(x-7)

rArr(x^2-13x+42)/(x+7)

=((x-6)(x-7))/(x+7)larrcolor(red)"in simplest form"

May 12, 2018

Restriction: x \ne -7 , simplified expression: Already simplified

Explanation:

since the denominator is x+7 and you cannot divide by zero, x+7 \ne 0 thus, x \ne -7
next because the expression on the numerator is a quadratic, it can probably be factored. All that is needed is two numbers that add up to -13 ad two numbers that multiply to 42.

If you factor 42 you get: \pm[1,2,3,6,7,14,21,42]
notice that -6 and -7 add up to -13 and multiply to 42 thus:

x^2-13x+42 = x^2-6x-7x+42 = x(x-6) -7(x-6) = (x-6)(x-7)

None of these linear factors cancel out with the denominator and thus the expression cannot be simplified.