How do I simplify a binomial division?

[pleasehelpme6]

Homework Statement

(v-4)/(5v+1)

The Attempt at a Solution

I'm an engineering student, and I'm taking Differential Equations, but I can't remember how to do simple things like this.

A walk through explanation would be very much appreciated, I don't have a lot of time to spare.

The simplification I need to arrive at is = 1/5 - 21/(5*(5v+1))

The solution I've come up with is 1/5 - 42/(5v+1)

Can anyone help? Thanks

 

[symbolipoint]

The process is fundamentally the same as ordinary base-ten division using expanded form.

v vidided by 5v is 1/5. Multiply 1/5 by (5v+1), subtract from (v-4). Remainder is -4.2, but would be, "negative four and one fifth", in mixed number form.
My result seems to be (1/5)-4&(1/5)/(5v+1).
$\frac{1}{5}-4\frac{1}{5}/(5v+1)$, seems TeX is not working.
$\frac{}{}-\frac{}{}$