ປະເມີນ
\frac{x^{3}-5x^{2}+9x+1}{\left(x^{2}-1\right)\left(x^{2}-x+1\right)}
ຂະຫຍາຍ
\frac{x^{3}-5x^{2}+9x+1}{\left(x^{2}-1\right)\left(x^{2}-x+1\right)}
Graph
ແບ່ງປັນ
ສໍາເນົາຄລິບ
\frac{1}{x-1}+\frac{3x+1}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+6x-1}{1+x^{3}}
ຕົວປະກອບ x^{2}-1.
\frac{x+1}{\left(x-1\right)\left(x+1\right)}+\frac{3x+1}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+6x-1}{1+x^{3}}
ເພື່ອເພີ່ມ ຫຼື ຫານນິພົດ, ໃຫ້ຂະຫຍາຍພວກມັນເພື່ອໃຫ້ຕົວຄູນມີຈຳນວນດຽວກັນ. ຈຳນວນຄູນທີ່ນິຍົມໜ້ອຍທີ່ສຸດຂອງ x-1 ກັບ \left(x-1\right)\left(x+1\right) ແມ່ນ \left(x-1\right)\left(x+1\right). ຄູນ \frac{1}{x-1} ໃຫ້ກັບ \frac{x+1}{x+1}.
\frac{x+1+3x+1}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+6x-1}{1+x^{3}}
ເນື່ອງຈາກ \frac{x+1}{\left(x-1\right)\left(x+1\right)} ແລະ \frac{3x+1}{\left(x-1\right)\left(x+1\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ເພີ່ມພວກມັນໂດຍການເພີ່ມຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.
\frac{4x+2}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+6x-1}{1+x^{3}}
ຮວມຂໍ້ກຳນົດໃນ x+1+3x+1.
\frac{4x+2}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+6x-1}{\left(x+1\right)\left(x^{2}-x+1\right)}
ຕົວປະກອບ 1+x^{3}.
\frac{\left(4x+2\right)\left(x^{2}-x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right)}-\frac{\left(3x^{2}+6x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right)}
ເພື່ອເພີ່ມ ຫຼື ຫານນິພົດ, ໃຫ້ຂະຫຍາຍພວກມັນເພື່ອໃຫ້ຕົວຄູນມີຈຳນວນດຽວກັນ. ຈຳນວນຄູນທີ່ນິຍົມໜ້ອຍທີ່ສຸດຂອງ \left(x-1\right)\left(x+1\right) ກັບ \left(x+1\right)\left(x^{2}-x+1\right) ແມ່ນ \left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right). ຄູນ \frac{4x+2}{\left(x-1\right)\left(x+1\right)} ໃຫ້ກັບ \frac{x^{2}-x+1}{x^{2}-x+1}. ຄູນ \frac{3x^{2}+6x-1}{\left(x+1\right)\left(x^{2}-x+1\right)} ໃຫ້ກັບ \frac{x-1}{x-1}.
\frac{\left(4x+2\right)\left(x^{2}-x+1\right)-\left(3x^{2}+6x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right)}
ເນື່ອງຈາກ \frac{\left(4x+2\right)\left(x^{2}-x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right)} ແລະ \frac{\left(3x^{2}+6x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ຫານພວກມັນໂດຍການຫານຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.
\frac{4x^{3}-4x^{2}+4x+2x^{2}-2x+2-3x^{3}+3x^{2}-6x^{2}+6x+x-1}{\left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right)}
ຄູນໃນເສດສ່ວນ \left(4x+2\right)\left(x^{2}-x+1\right)-\left(3x^{2}+6x-1\right)\left(x-1\right).
\frac{x^{3}-5x^{2}+9x+1}{\left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right)}
ຮວມຂໍ້ກຳນົດໃນ 4x^{3}-4x^{2}+4x+2x^{2}-2x+2-3x^{3}+3x^{2}-6x^{2}+6x+x-1.
\frac{x^{3}-5x^{2}+9x+1}{x^{4}-x^{3}+x-1}
ຂະຫຍາຍ \left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right).
\frac{1}{x-1}+\frac{3x+1}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+6x-1}{1+x^{3}}
ຕົວປະກອບ x^{2}-1.
\frac{x+1}{\left(x-1\right)\left(x+1\right)}+\frac{3x+1}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+6x-1}{1+x^{3}}
ເພື່ອເພີ່ມ ຫຼື ຫານນິພົດ, ໃຫ້ຂະຫຍາຍພວກມັນເພື່ອໃຫ້ຕົວຄູນມີຈຳນວນດຽວກັນ. ຈຳນວນຄູນທີ່ນິຍົມໜ້ອຍທີ່ສຸດຂອງ x-1 ກັບ \left(x-1\right)\left(x+1\right) ແມ່ນ \left(x-1\right)\left(x+1\right). ຄູນ \frac{1}{x-1} ໃຫ້ກັບ \frac{x+1}{x+1}.
\frac{x+1+3x+1}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+6x-1}{1+x^{3}}
ເນື່ອງຈາກ \frac{x+1}{\left(x-1\right)\left(x+1\right)} ແລະ \frac{3x+1}{\left(x-1\right)\left(x+1\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ເພີ່ມພວກມັນໂດຍການເພີ່ມຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.
\frac{4x+2}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+6x-1}{1+x^{3}}
ຮວມຂໍ້ກຳນົດໃນ x+1+3x+1.
\frac{4x+2}{\left(x-1\right)\left(x+1\right)}-\frac{3x^{2}+6x-1}{\left(x+1\right)\left(x^{2}-x+1\right)}
ຕົວປະກອບ 1+x^{3}.
\frac{\left(4x+2\right)\left(x^{2}-x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right)}-\frac{\left(3x^{2}+6x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right)}
ເພື່ອເພີ່ມ ຫຼື ຫານນິພົດ, ໃຫ້ຂະຫຍາຍພວກມັນເພື່ອໃຫ້ຕົວຄູນມີຈຳນວນດຽວກັນ. ຈຳນວນຄູນທີ່ນິຍົມໜ້ອຍທີ່ສຸດຂອງ \left(x-1\right)\left(x+1\right) ກັບ \left(x+1\right)\left(x^{2}-x+1\right) ແມ່ນ \left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right). ຄູນ \frac{4x+2}{\left(x-1\right)\left(x+1\right)} ໃຫ້ກັບ \frac{x^{2}-x+1}{x^{2}-x+1}. ຄູນ \frac{3x^{2}+6x-1}{\left(x+1\right)\left(x^{2}-x+1\right)} ໃຫ້ກັບ \frac{x-1}{x-1}.
\frac{\left(4x+2\right)\left(x^{2}-x+1\right)-\left(3x^{2}+6x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right)}
ເນື່ອງຈາກ \frac{\left(4x+2\right)\left(x^{2}-x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right)} ແລະ \frac{\left(3x^{2}+6x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ຫານພວກມັນໂດຍການຫານຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.
\frac{4x^{3}-4x^{2}+4x+2x^{2}-2x+2-3x^{3}+3x^{2}-6x^{2}+6x+x-1}{\left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right)}
ຄູນໃນເສດສ່ວນ \left(4x+2\right)\left(x^{2}-x+1\right)-\left(3x^{2}+6x-1\right)\left(x-1\right).
\frac{x^{3}-5x^{2}+9x+1}{\left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right)}
ຮວມຂໍ້ກຳນົດໃນ 4x^{3}-4x^{2}+4x+2x^{2}-2x+2-3x^{3}+3x^{2}-6x^{2}+6x+x-1.
\frac{x^{3}-5x^{2}+9x+1}{x^{4}-x^{3}+x-1}
ຂະຫຍາຍ \left(x-1\right)\left(x+1\right)\left(x^{2}-x+1\right).
ຕົວຢ່າງ
ສະສົມQuadratic
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
ສະສົມເສັ້ນ
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
ສະສົມພ້ອມກັນ
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
ຄວາມແຕກແຍກ
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
ການຮວມ
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
ຂີດຈໍາກັດ
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}