√10+√14-√15-√21/√10+√14+√15+√21
=√10+√14-√15-√21/√10+√14+√15+√21
=(√5(√2-√3)+√7(√2-√3))/(√5(√2+√3)+√7(√2+√3))
=(√5+√7)(√2-√3)/(√5+√7)(√2+√3)
=(√2-√3)/(√2+√3)
=(√2-√3)^2/(√2+√3)(√2-√3)
=(2-2√6+3)/(2-3)
=2√6-5
√10+√14-√15-√21/√10+√14+√15+√21
=√10+√14-√15-√21/√10+√14+√15+√21
=(√5(√2-√3)+√7(√2-√3))/(√5(√2+√3)+√7(√2+√3))
=(√5+√7)(√2-√3)/(√5+√7)(√2+√3)
=(√2-√3)/(√2+√3)
=(√2-√3)^2/(√2+√3)(√2-√3)
=(2-2√6+3)/(2-3)
=2√6-5