maths questions about functions?

Question

the function f is defined as f(x) = 2x+3 / x-1 when x is not 1

xpress f(x) in the form f(X) = a + (b/x-1)

wer a and b are constants

Answer 1

f(x) = 2x+3/x-1
= (2x-2+5)/(x-1)
= (2x-2)/(x-1) + 5/x-1
= 2(x-1)/ (x-1) + 5/x-1

= 2 + 5/x-1

Hence, a = 2 and b = 5

Answer 2

you can write 2x+3 = 2(x-1) +5

so 2x+3/(x-1) = (2(x-1)+5)/(x-1) = 2+5/(x-1)

so a=2 and b=5