Question

If g(x)= x+1/x-2 and h(x)=4-x, what is the value of (g o h)(-3)? I keep getting 14/5... What am I doing wrong? Answer choices are : 8/5 5/2 15/2 18/5

Answer 1

Simply divide the right side of $g(x)$ expression over the right side of $h(x)$ expression:
$\frac{g}{h}(x)=\frac{x+\frac{1}{x}-2}{4-x}$

Now, replace variable $x$ in found eqpression with -3:
$\frac{g}{h}(-3)=\frac{-3+\frac{1}{-3}-2}{4-(-3)}=\frac{-5-\frac{1}{3}}{7}=-\frac{\frac{15+1}{3}}{7}=-\frac{16}{3*7}=-\frac{16}{21}$