ປະເມີນ
\frac{x}{x^{2}-x+1}
ຂະຫຍາຍ
\frac{x}{x^{2}-x+1}
Graph
ແບ່ງປັນ
ສໍາເນົາຄລິບ
\frac{\left(x-2\right)\left(x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)}-\frac{x^{2}-x+1}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+1}
ເພື່ອເພີ່ມ ຫຼື ຫານນິພົດ, ໃຫ້ຂະຫຍາຍພວກມັນເພື່ອໃຫ້ຕົວຄູນມີຈຳນວນດຽວກັນ. ຈຳນວນຄູນທີ່ນິຍົມໜ້ອຍທີ່ສຸດຂອງ x^{2}-x+1 ກັບ x+1 ແມ່ນ \left(x+1\right)\left(x^{2}-x+1\right). ຄູນ \frac{x-2}{x^{2}-x+1} ໃຫ້ກັບ \frac{x+1}{x+1}. ຄູນ \frac{1}{x+1} ໃຫ້ກັບ \frac{x^{2}-x+1}{x^{2}-x+1}.
\frac{\left(x-2\right)\left(x+1\right)-\left(x^{2}-x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+1}
ເນື່ອງຈາກ \frac{\left(x-2\right)\left(x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)} ແລະ \frac{x^{2}-x+1}{\left(x+1\right)\left(x^{2}-x+1\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ຫານພວກມັນໂດຍການຫານຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.
\frac{x^{2}+x-2x-2-x^{2}+x-1}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+1}
ຄູນໃນເສດສ່ວນ \left(x-2\right)\left(x+1\right)-\left(x^{2}-x+1\right).
\frac{-3}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+1}
ຮວມຂໍ້ກຳນົດໃນ x^{2}+x-2x-2-x^{2}+x-1.
\frac{-3}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{\left(x+1\right)\left(x^{2}-x+1\right)}
ຕົວປະກອບ x^{3}+1.
\frac{-3+x^{2}+x+3}{\left(x+1\right)\left(x^{2}-x+1\right)}
ເນື່ອງຈາກ \frac{-3}{\left(x+1\right)\left(x^{2}-x+1\right)} ແລະ \frac{x^{2}+x+3}{\left(x+1\right)\left(x^{2}-x+1\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ເພີ່ມພວກມັນໂດຍການເພີ່ມຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.
\frac{x^{2}+x}{\left(x+1\right)\left(x^{2}-x+1\right)}
ຮວມຂໍ້ກຳນົດໃນ -3+x^{2}+x+3.
\frac{x\left(x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)}
ປັດໃຈທີ່ນິພົດບໍ່ມີຢູ່ໃນ \frac{x^{2}+x}{\left(x+1\right)\left(x^{2}-x+1\right)}.
\frac{x}{x^{2}-x+1}
ຍົກເລີກ x+1 ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.
\frac{\left(x-2\right)\left(x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)}-\frac{x^{2}-x+1}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+1}
ເພື່ອເພີ່ມ ຫຼື ຫານນິພົດ, ໃຫ້ຂະຫຍາຍພວກມັນເພື່ອໃຫ້ຕົວຄູນມີຈຳນວນດຽວກັນ. ຈຳນວນຄູນທີ່ນິຍົມໜ້ອຍທີ່ສຸດຂອງ x^{2}-x+1 ກັບ x+1 ແມ່ນ \left(x+1\right)\left(x^{2}-x+1\right). ຄູນ \frac{x-2}{x^{2}-x+1} ໃຫ້ກັບ \frac{x+1}{x+1}. ຄູນ \frac{1}{x+1} ໃຫ້ກັບ \frac{x^{2}-x+1}{x^{2}-x+1}.
\frac{\left(x-2\right)\left(x+1\right)-\left(x^{2}-x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+1}
ເນື່ອງຈາກ \frac{\left(x-2\right)\left(x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)} ແລະ \frac{x^{2}-x+1}{\left(x+1\right)\left(x^{2}-x+1\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ຫານພວກມັນໂດຍການຫານຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.
\frac{x^{2}+x-2x-2-x^{2}+x-1}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+1}
ຄູນໃນເສດສ່ວນ \left(x-2\right)\left(x+1\right)-\left(x^{2}-x+1\right).
\frac{-3}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{x^{3}+1}
ຮວມຂໍ້ກຳນົດໃນ x^{2}+x-2x-2-x^{2}+x-1.
\frac{-3}{\left(x+1\right)\left(x^{2}-x+1\right)}+\frac{x^{2}+x+3}{\left(x+1\right)\left(x^{2}-x+1\right)}
ຕົວປະກອບ x^{3}+1.
\frac{-3+x^{2}+x+3}{\left(x+1\right)\left(x^{2}-x+1\right)}
ເນື່ອງຈາກ \frac{-3}{\left(x+1\right)\left(x^{2}-x+1\right)} ແລະ \frac{x^{2}+x+3}{\left(x+1\right)\left(x^{2}-x+1\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ເພີ່ມພວກມັນໂດຍການເພີ່ມຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.
\frac{x^{2}+x}{\left(x+1\right)\left(x^{2}-x+1\right)}
ຮວມຂໍ້ກຳນົດໃນ -3+x^{2}+x+3.
\frac{x\left(x+1\right)}{\left(x+1\right)\left(x^{2}-x+1\right)}
ປັດໃຈທີ່ນິພົດບໍ່ມີຢູ່ໃນ \frac{x^{2}+x}{\left(x+1\right)\left(x^{2}-x+1\right)}.
\frac{x}{x^{2}-x+1}
ຍົກເລີກ x+1 ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.
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