First, multiply the fraction on the left by the appropriate form of #1# (in this problem #2/2) to have both fractions over a common denominator so they can be subtracted:
#(2/2 xx 14/5) - (2sqrt(6))/10 => 28/10 - (2sqrt(6))/10#
Next, subtract the numerators over the common denominator:
#(28 - 2sqrt(6))/10#
Next, factor a #2# out of each term in the numerator and cancel common terms in the numerator and denominator:
#((2 * 14) - (2 * sqrt(6)))/(2 * 5) => (2(14 - sqrt(6)))/(2 * 5) => (color(red)(cancel(color(black)(2)))(14 - sqrt(6)))/(color(red)(cancel(color(black)(2))) * 5) =>#
#(14 - sqrt(6))/5#
A second process would be to first factor out a #2# from each term in the fraction on the right:
#14/5 - (2 * sqrt(6))/(2 * 5) => 14/5 - (color(red)(cancel(color(black)(2))) * sqrt(6))/(color(red)(cancel(color(black)(2))) * 5) => 14/5 - sqrt(6)/5#
Now, subtract the two numerators over the common denominator:
#(14 - sqrt(6))/5#
