ປະເມີນ
-\frac{2}{x^{2}}
ຂະຫຍາຍ
-\frac{2}{x^{2}}
Graph
ແບ່ງປັນ
ສໍາເນົາຄລິບ
\frac{\frac{x+1}{\left(x+1\right)\left(-x+1\right)}-\frac{-x+1}{\left(x+1\right)\left(-x+1\right)}}{\frac{x}{x^{2}-1}+x}
ເພື່ອເພີ່ມ ຫຼື ຫານນິພົດ, ໃຫ້ຂະຫຍາຍພວກມັນເພື່ອໃຫ້ຕົວຄູນມີຈຳນວນດຽວກັນ. ຈຳນວນຄູນທີ່ນິຍົມໜ້ອຍທີ່ສຸດຂອງ 1-x ກັບ 1+x ແມ່ນ \left(x+1\right)\left(-x+1\right). ຄູນ \frac{1}{1-x} ໃຫ້ກັບ \frac{x+1}{x+1}. ຄູນ \frac{1}{1+x} ໃຫ້ກັບ \frac{-x+1}{-x+1}.
\frac{\frac{x+1-\left(-x+1\right)}{\left(x+1\right)\left(-x+1\right)}}{\frac{x}{x^{2}-1}+x}
ເນື່ອງຈາກ \frac{x+1}{\left(x+1\right)\left(-x+1\right)} ແລະ \frac{-x+1}{\left(x+1\right)\left(-x+1\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ຫານພວກມັນໂດຍການຫານຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.
\frac{\frac{x+1+x-1}{\left(x+1\right)\left(-x+1\right)}}{\frac{x}{x^{2}-1}+x}
ຄູນໃນເສດສ່ວນ x+1-\left(-x+1\right).
\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x}{x^{2}-1}+x}
ຮວມຂໍ້ກຳນົດໃນ x+1+x-1.
\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x}{\left(x-1\right)\left(x+1\right)}+x}
ຕົວປະກອບ x^{2}-1.
\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x}{\left(x-1\right)\left(x+1\right)}+\frac{x\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}}
ເພື່ອເພີ່ມ ຫຼື ຫານນິພົດ, ໃຫ້ຂະຫຍາຍພວກມັນເພື່ອໃຫ້ຕົວຄູນມີຈຳນວນດຽວກັນ. ຄູນ x ໃຫ້ກັບ \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.
\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x+x\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}}
ເນື່ອງຈາກ \frac{x}{\left(x-1\right)\left(x+1\right)} ແລະ \frac{x\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ເພີ່ມພວກມັນໂດຍການເພີ່ມຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.
\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x+x^{3}+x^{2}-x^{2}-x}{\left(x-1\right)\left(x+1\right)}}
ຄູນໃນເສດສ່ວນ x+x\left(x-1\right)\left(x+1\right).
\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}
ຮວມຂໍ້ກຳນົດໃນ x+x^{3}+x^{2}-x^{2}-x.
\frac{2x\left(x-1\right)\left(x+1\right)}{\left(x+1\right)\left(-x+1\right)x^{3}}
ຫານ \frac{2x}{\left(x+1\right)\left(-x+1\right)} ດ້ວຍ \frac{x^{3}}{\left(x-1\right)\left(x+1\right)} ໂດຍການຄູນ \frac{2x}{\left(x+1\right)\left(-x+1\right)} ໂດຍຕົວເລກທີ່ກັບກັນຂອງ \frac{x^{3}}{\left(x-1\right)\left(x+1\right)}.
\frac{-2x\left(x+1\right)\left(-x+1\right)}{\left(x+1\right)\left(-x+1\right)x^{3}}
ແຍກເຄື່ອງໝາຍລົບໃນ x-1.
\frac{-2}{x^{2}}
ຍົກເລີກ x\left(x+1\right)\left(-x+1\right) ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.
\frac{\frac{x+1}{\left(x+1\right)\left(-x+1\right)}-\frac{-x+1}{\left(x+1\right)\left(-x+1\right)}}{\frac{x}{x^{2}-1}+x}
ເພື່ອເພີ່ມ ຫຼື ຫານນິພົດ, ໃຫ້ຂະຫຍາຍພວກມັນເພື່ອໃຫ້ຕົວຄູນມີຈຳນວນດຽວກັນ. ຈຳນວນຄູນທີ່ນິຍົມໜ້ອຍທີ່ສຸດຂອງ 1-x ກັບ 1+x ແມ່ນ \left(x+1\right)\left(-x+1\right). ຄູນ \frac{1}{1-x} ໃຫ້ກັບ \frac{x+1}{x+1}. ຄູນ \frac{1}{1+x} ໃຫ້ກັບ \frac{-x+1}{-x+1}.
\frac{\frac{x+1-\left(-x+1\right)}{\left(x+1\right)\left(-x+1\right)}}{\frac{x}{x^{2}-1}+x}
ເນື່ອງຈາກ \frac{x+1}{\left(x+1\right)\left(-x+1\right)} ແລະ \frac{-x+1}{\left(x+1\right)\left(-x+1\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ຫານພວກມັນໂດຍການຫານຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.
\frac{\frac{x+1+x-1}{\left(x+1\right)\left(-x+1\right)}}{\frac{x}{x^{2}-1}+x}
ຄູນໃນເສດສ່ວນ x+1-\left(-x+1\right).
\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x}{x^{2}-1}+x}
ຮວມຂໍ້ກຳນົດໃນ x+1+x-1.
\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x}{\left(x-1\right)\left(x+1\right)}+x}
ຕົວປະກອບ x^{2}-1.
\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x}{\left(x-1\right)\left(x+1\right)}+\frac{x\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}}
ເພື່ອເພີ່ມ ຫຼື ຫານນິພົດ, ໃຫ້ຂະຫຍາຍພວກມັນເພື່ອໃຫ້ຕົວຄູນມີຈຳນວນດຽວກັນ. ຄູນ x ໃຫ້ກັບ \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.
\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x+x\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}}
ເນື່ອງຈາກ \frac{x}{\left(x-1\right)\left(x+1\right)} ແລະ \frac{x\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ເພີ່ມພວກມັນໂດຍການເພີ່ມຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.
\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x+x^{3}+x^{2}-x^{2}-x}{\left(x-1\right)\left(x+1\right)}}
ຄູນໃນເສດສ່ວນ x+x\left(x-1\right)\left(x+1\right).
\frac{\frac{2x}{\left(x+1\right)\left(-x+1\right)}}{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}
ຮວມຂໍ້ກຳນົດໃນ x+x^{3}+x^{2}-x^{2}-x.
\frac{2x\left(x-1\right)\left(x+1\right)}{\left(x+1\right)\left(-x+1\right)x^{3}}
ຫານ \frac{2x}{\left(x+1\right)\left(-x+1\right)} ດ້ວຍ \frac{x^{3}}{\left(x-1\right)\left(x+1\right)} ໂດຍການຄູນ \frac{2x}{\left(x+1\right)\left(-x+1\right)} ໂດຍຕົວເລກທີ່ກັບກັນຂອງ \frac{x^{3}}{\left(x-1\right)\left(x+1\right)}.
\frac{-2x\left(x+1\right)\left(-x+1\right)}{\left(x+1\right)\left(-x+1\right)x^{3}}
ແຍກເຄື່ອງໝາຍລົບໃນ x-1.
\frac{-2}{x^{2}}
ຍົກເລີກ x\left(x+1\right)\left(-x+1\right) ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.
ຕົວຢ່າງ
ສະສົມQuadratic
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y = 3x + 4
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\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
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\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}