(a) Write down the first three terms of the binomial expansion of \( (1+t)^{-1} \) in ascending powers of \( t \).

(b) \( \frac{3}{x-1}<\frac{2}{x} \)

8. \( \frac{\sqrt{27 a^{3} b^{6}}}{\sqrt{3 a b^{6}}-5 a b^{2}}= \)

a. \( \frac{2 x^{3}+6 x-6}{x^{3}-1} \)

In the \( x y \)-plane, a parabola has vertex \( (9,-14) \) and intersects the \( x \)-axis at two points. If the equation of the parabola is written in the form \( y=a x^{2}+b x+c \) where \( a, b \), and \( c \) are constants, which of the following could be the value of \( a+b+c \) ? (A) -23 (B) -19 (D) -12

1) \( \frac{10 x+8}{3 a-b}-\frac{9 x+5}{3 a-b}= \)