How do you find the excluded value and simplify # (x^2-13x+42)/(x+7)#?
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 "#
#"the factors of + 42 which sum to - 13 are - 6 and - 7"#
#=((x-6)(x-7))/(x+7)larrcolor(red)"in simplest form"#
since the denominator is
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:
notice that -6 and -7 add up to -13 and multiply to 42 thus:
None of these linear factors cancel out with the denominator and thus the expression cannot be simplified.