What's the function equation in the form of that ?

Question

Let f(x)={3x-5}/{x-2}

Write the function equation in the form of f(x)=q(x)+r(x)/d(x)

Answer 1

You have to do the polynomial long division:

_____3_

x-2 ) 3x - 5

-(3x-6)

------------

1

So the quotient (q(x)) is 3, the remainder (r(x)) is 1 and we put the remainder over the divisor (d(x)) x-2:

q(x) + r(x)/d(x) = 3 + 1/(x-2)