Answer
Evaluate $h(t) = t + \frac{1}{t}$:
$h(-1) = -2$
$h(2) =\frac{5}{2} = 2.5 $
$h(\frac{1}{2}) =\frac{5}{2} = 2.5 $
$h(x-1) = (x-1) + \frac{1}{x-1} = \frac{x^2-2x+2}{x-1}$
$h(\frac{1}{x}) = \frac{1}{x} + x = \frac{x^{2}+1}{x}$
Work Step by Step
for $t = -1$
$h(-1) = (-1) + \frac{1}{-1}$... simplify fraction
$= (-1) + (-1)$... add
$=-2 $
_____________________
for $t = 2$
$h(2) = (2) + \frac{1}{2}$... convert whole number to fraction with common denominator
$= \frac {4}{2} + \frac{1}{2}$... add
$=\frac{5}{2} = 2.5 $
_____________________
for $t = \frac{1}{2}$
$h(\frac{1}{2}) = \frac{1}{2} + \frac{1}{\frac{1}{2}}$... simplify complex fraction
$= \frac{1}{2} + 2$... convert whole number to fraction with common denominator
$=\frac{1}{2} + \frac{4}{2} $ ...add
$=\frac{5}{2}=2.5$
_____________________
for $t = x-1$
$h(x-1) = (x-1) + \frac{1}{x-1}$... convert polynomial to fraction with common denominator
$= \frac{(x-1)^2}{x-1} + \frac{1}{x-1}$... add
$= \frac{(x-1)^2+1}{x-1}$ ... square (x-1) and add 1
$= \frac{x^2-2x+2}{x-1}$
_____________________
for $t = \frac{1}{x}$
$h(\frac{1}{x}) = \frac{1}{x} + \frac{1}{\frac{1}{x}}$... simplify complex fraction
$= \frac{1}{x} + x$... convert variable to fraction with common denominator
$=\frac{1}{x} + \frac{x^{2}}{x} $ ...add
$=\frac{x^{2}+1}{x}$
_____________________