15-8akar3/ 8akar3-13

[tex] \frac{15 - 8 \sqrt{3} }{8 \sqrt{3} - 13 } \times \frac{8 \sqrt{3} + 13}{8 \sqrt{3} + 13} \\ = \frac{120 \sqrt{3} + 195 - 64 \times 3 - 104 \sqrt{3} }{64 \times 3 + 104 \sqrt{3} - 104 \sqrt{3} - 169 } \\ = \frac{16 \sqrt{3} + 195 - 192}{192 - 169} \\ = \frac{16 \sqrt{3} + 3}{23} [/tex]

15 - 8√3      8√3 + 13      15(8√3) + 15(13) - 8√3(8√3) - 8√3(13)
------------ x -------------- = ---------------------------------------------------
8√3 - 13      8√3 + 13                  8√3(8√3) - 13(13)

                                        120√3 + 195 - 192 - 104√3
                                    = --------------------------------------
                                             192 - 169
                                        
                                         16√3 + 3
                                     = -------------
                                             23