How do you write the mixed expression #t+(v+w)/(v-w)# as a rational expression?

1 Answer
NJ
May 11, 2018

#=(t(v-w) + (v+w))/(v-w)#

or

#=((1+t)v + (1-t)w)/(v-w)#

Explanation:

The key here is to obtain a common denominator. This can be done by multiplying the #t# by a factor of #1# so that the expression does not change. But we can write our #1# in a way that is useful.

#t + (v+w)/(v-w)#

#=t*(v-w)/(v-w) + (v+w)/(v-w)#

#=(t(v-w))/(v-w) + (v+w)/(v-w)#

#=(t(v-w) + (v+w))/(v-w)#

If you wanted to make sure #u# and #v# were only written once in the numerator, you could rearrange.

#=(tv - tw +v+w)/(v-w)#

#=((1+t)v + (1-t)w)/(v-w)#

Anything over a single denominator is considered a ration expression.

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