Question

How do you combine `(x-1)/x-(t+1)/t`?

Answer 1

`-(t+x)/(tx)`

Explanation:

To combine them you must have a denominator that is divisible by both `t` and `x`. The most obvious one it `tx`

Consider `(x-1)/x`

Multiply by 1 but in the form of `1=t/t`

`(x-1)/x xx t/t = (t(x-1))/(tx) = (tx-t)/(tx)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider `(t+1)/t`

Multiply by 1 but in the form of `1=x/x`

`(t+1)/x xx x/x=(x(t+1))/(tx) = (tx+x)/(tx)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Putting it all together

`(tx-t)/(tx) - (tx+x)/(tx)" " =" " (cancel(tx)-t-cancel(tx)-x)/(tx)`

`(-t-x)/(tx)" " =" " (-(t+x))/(tx)" " =" " -(t+x)/(tx)`