How would you answer these question

Question

Answer 1

g(x) = 2x - 1 / x - 3 = a / x - 3 + b

Multiply  each side by x - 3

2x - 1 = a  + b(x - 3)

2x - 1 = a + bx - 3b

2x - 1 = bx + a - 3b

Compare x coeficients and constant

b = 2 and  -1 = a - 3b

-1 = a - 3(2)

-1 = a - 6

Add 6 to each side

6-1 = a

a = 5

Substitute a = 5 and b = 2 in the above function

g(x) = 2x - 1 / x - 3 = (5 / x - 3) + 2.