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

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Answer 1 · 2016-07-10T15:35:02

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

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

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

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

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