Răspuns :
15/(8√2 -6√3) +20/(7√2 -4√3 )-4/(5√3-6√2)=
=15(8√2 +6√3)/(8√2 -6√3)(8√2 +6√3) +20(7√2 +4√3 )/(7√2 -4√3 )(7√2 +4√3 ) --4(5√3+6√2)/(5√3-6√2)(5√3+6√2)=
=(120√2 +90√3)/(128-108) +(140√2 +80√3 )/(98 -48)-(20√3+24√2)/(75-72)=
=(120√2 +90√3)/20 +(140√2 +80√3 )/50-(20√3+24√2)/3=
=(12√2 +9√3)/2 +(14√2 +8√3 )/5-(20√3-24√2)/3=
=(180√2 +135√3 +84√2 +48√3 -200√3-240√2)/30=
=(24√2-17√3)/30
=15(8√2 +6√3)/(8√2 -6√3)(8√2 +6√3) +20(7√2 +4√3 )/(7√2 -4√3 )(7√2 +4√3 ) --4(5√3+6√2)/(5√3-6√2)(5√3+6√2)=
=(120√2 +90√3)/(128-108) +(140√2 +80√3 )/(98 -48)-(20√3+24√2)/(75-72)=
=(120√2 +90√3)/20 +(140√2 +80√3 )/50-(20√3+24√2)/3=
=(12√2 +9√3)/2 +(14√2 +8√3 )/5-(20√3-24√2)/3=
=(180√2 +135√3 +84√2 +48√3 -200√3-240√2)/30=
=(24√2-17√3)/30
[tex]\displaystyle \frac{15}{8 \sqrt{2} -6 \sqrt{3} } + \frac{20}{7 \sqrt{2} -4 \sqrt{3} } - \frac{4}{5 \sqrt{3} -6 \sqrt{2} } = \\ \\ = \frac{15(8 \sqrt{2} +6 \sqrt{3} )}{128-108} + \frac{20(7 \sqrt{2} +4 \sqrt{3} )}{98-48} - \frac{4(5 \sqrt{3} +6 \sqrt{2} )}{75-72} = \\ = \frac{15(8 \sqrt{2} +6 \sqrt{3} )}{20} + \frac{20(7 \sqrt{2} +4 \sqrt{3} )}{50} - \frac{4(5 \sqrt{3} +6 \sqrt{2} )}{3} =[/tex]
[tex]\displaystyle = \frac{3(8 \sqrt{2}+6 \sqrt{3}) }{4} + \frac{2(7 \sqrt{2} +4 \sqrt{3} )}{5} - \frac{4(5 \sqrt{3} +6 \sqrt{2}) }{3} = \\ \\ = \frac{24 \sqrt{2} +18 \sqrt{3} }{4} + \frac{14 \sqrt{2} +8 \sqrt{3} }{5} - \frac{20 \sqrt{3} +24 \sqrt{2} }{3} = \\ \\ = \frac{15(24 \sqrt{2} +18 \sqrt{3} )+12(14 \sqrt{2} +8 \sqrt{3} )-20(20 \sqrt{3} +24 \sqrt{2} )}{60} = [/tex]
[tex]\displaystyle = \frac{360 \sqrt{2}+270 \sqrt{3} +168 \sqrt{2} + 96 \sqrt{3} -400 \sqrt{3} -480 \sqrt{2} }{60} = \\ \\ = \frac{48 \sqrt{2}- 34 \sqrt{3} }{60} = \frac{2(24 \sqrt{2} -17 \sqrt{3} )}{60} = \frac{24 \sqrt{2} -17 \sqrt{3} }{30} [/tex]
[tex]\displaystyle = \frac{3(8 \sqrt{2}+6 \sqrt{3}) }{4} + \frac{2(7 \sqrt{2} +4 \sqrt{3} )}{5} - \frac{4(5 \sqrt{3} +6 \sqrt{2}) }{3} = \\ \\ = \frac{24 \sqrt{2} +18 \sqrt{3} }{4} + \frac{14 \sqrt{2} +8 \sqrt{3} }{5} - \frac{20 \sqrt{3} +24 \sqrt{2} }{3} = \\ \\ = \frac{15(24 \sqrt{2} +18 \sqrt{3} )+12(14 \sqrt{2} +8 \sqrt{3} )-20(20 \sqrt{3} +24 \sqrt{2} )}{60} = [/tex]
[tex]\displaystyle = \frac{360 \sqrt{2}+270 \sqrt{3} +168 \sqrt{2} + 96 \sqrt{3} -400 \sqrt{3} -480 \sqrt{2} }{60} = \\ \\ = \frac{48 \sqrt{2}- 34 \sqrt{3} }{60} = \frac{2(24 \sqrt{2} -17 \sqrt{3} )}{60} = \frac{24 \sqrt{2} -17 \sqrt{3} }{30} [/tex]