Can someone help me solve this? Thanks!
1 Answer
Explanation:
#"factorise and simplify"#
#y=(cancel((x-5)))/(cancel((x-5))(x-1))=1/(x-1)#
#"since we have removed the factor "(x-5)#
#"from the numerator/denominator this indicates a"#
#"hole"#
#x-5=0rArrx=5" and "y=1/(5-1)=1/4#
The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote.
#"solve "x-1=0rArrx=1" is the asymptote"#
#" the asymptote is non-removable"#
graph{1/(x-1) [-10, 10, -5, 5]}
#"the graph of "y=(x-5)/(x^2-6x+5)" but without the hole"#