Find the vertical asymptotes of {{MATH_161}} {{CMD_162}} The domain of the numerator, {{MATH_163}}, is {{MATH_164}} and it is continuous on that entire interval. The denominator, {{MATH_165}}, is continuous on {{MATH_166}}, and is zero only at {{MATH_167}}. That makes the domain of {{MATH_168}} to be {{MATH_169}}, and {{MATH_170}} is continuous on this interval. There is only one {{MATH_171}}-value where {{MATH_172}} could have a vertical asymptote: at {{MATH_173}}. It is not in the domain of {{MATH_174}}, but is approachable from within the domain. Where the denominator is zero, {{MATH_175}} is NOT a possibility because {{MATH_176}} cannot be approached from within {{MATH_177}} due to the gap in the number line between {{MATH_178}} and {{MATH_179}}. Since we can only approach {{MATH_180}} from the right (while staying in the domain of {{MATH_181}}), we should examine the right-hand limit: {{MATH_182}} For the numerator we have {{MATH_183}}, while for the denominator we have {{MATH_184}}. This means {{MATH_185}}. There is a vertical asymptote at {{MATH_186}}. There are no others because {{MATH_187}} is continuous on its domain {{MATH_188}}.