Given: #2/(7x-14) and x/(3x-6)#

Notice that both 7 from #7x# and 3 from #3x# are prime numbers. As these are the #x# terms we will need to focus on those and just see what happens with the constants

I imagine that that the school would expect you to do it like this:

#color(white)("dddddddddddddddd") ubrace(3xx7)#

Multiples of 7 #->color(green)(7,14,color(red)(21),28," etc")#

Multiples of 3 #->color(green)(3,6,9,12,15,18,color(red)(21),24," etc")#

#color(white)("ddddddddddddddddddddddddd")obrace(7xx3)#

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

#color(green)([2/(7x-14)color(red)(xx1) ]and [x/(3x-6)color(red)(xx1)])#

#color(green)([2/(7x-14)color(red)(xx3/3) ]and [x/(3x-6)color(red)(xx7/7)])#

#color(white)("d")color(green)([6/(21x-42)]color(white)("dd")and color(white)("dd")[(7x)/(21x-42)] #

Consider just the denominator #21x-42#

Notice that #2xx21=42# so we can write it as #21(x-2)#