ແກ້ 2/x^2-x+5/x^2-x^3+3/x^2-1

$$\frac { 2 } { x ^ { 2 } - x } + \frac { 5 } { x ^ { 2 } - x ^ { 3 } } + \frac { 3 } { x ^ { 2 } - 1 }$$

ປະເມີນ

$$\frac{5+3x-5x^{2}}{x^{2}\left(1-x^{2}\right)}$$

ຂັ້ນຕອນທາງອອກສັ້ນ

ຕົວປະກອບ x^{2}-x. ຕົວປະກອບ x^{2}-x^{3}.

$$\frac{2}{x\left(x-1\right)}+\frac{5}{\left(-x+1\right)x^{2}}+\frac{3}{x^{2}-1}$$

ເພື່ອເພີ່ມ ຫຼື ຫານນິພົດ, ໃຫ້ຂະຫຍາຍພວກມັນເພື່ອໃຫ້ຕົວຄູນມີຈຳນວນດຽວກັນ. ຈຳນວນຄູນທີ່ນິຍົມໜ້ອຍທີ່ສຸດຂອງ x\left(x-1\right) ກັບ \left(-x+1\right)x^{2} ແມ່ນ \left(x-1\right)x^{2}. ຄູນ \frac{2}{x\left(x-1\right)} ໃຫ້ກັບ \frac{x}{x}. ຄູນ \frac{5}{\left(-x+1\right)x^{2}} ໃຫ້ກັບ \frac{-1}{-1}.

$$\frac{2x}{\left(x-1\right)x^{2}}+\frac{5\left(-1\right)}{\left(x-1\right)x^{2}}+\frac{3}{x^{2}-1}$$

ເນື່ອງຈາກ \frac{2x}{\left(x-1\right)x^{2}} ແລະ \frac{5\left(-1\right)}{\left(x-1\right)x^{2}} ມີຕົວຫານດຽວກັນ, ໃຫ້ເພີ່ມພວກມັນໂດຍການເພີ່ມຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.

$$\frac{2x+5\left(-1\right)}{\left(x-1\right)x^{2}}+\frac{3}{x^{2}-1}$$

ຄູນໃນເສດສ່ວນ 2x+5\left(-1\right).

$$\frac{2x-5}{\left(x-1\right)x^{2}}+\frac{3}{x^{2}-1}$$

ຕົວປະກອບ x^{2}-1.

$$\frac{2x-5}{\left(x-1\right)x^{2}}+\frac{3}{\left(x-1\right)\left(x+1\right)}$$

ເພື່ອເພີ່ມ ຫຼື ຫານນິພົດ, ໃຫ້ຂະຫຍາຍພວກມັນເພື່ອໃຫ້ຕົວຄູນມີຈຳນວນດຽວກັນ. ຈຳນວນຄູນທີ່ນິຍົມໜ້ອຍທີ່ສຸດຂອງ \left(x-1\right)x^{2} ກັບ \left(x-1\right)\left(x+1\right) ແມ່ນ \left(x-1\right)\left(x+1\right)x^{2}. ຄູນ \frac{2x-5}{\left(x-1\right)x^{2}} ໃຫ້ກັບ \frac{x+1}{x+1}. ຄູນ \frac{3}{\left(x-1\right)\left(x+1\right)} ໃຫ້ກັບ \frac{x^{2}}{x^{2}}.

$$\frac{\left(2x-5\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)x^{2}}+\frac{3x^{2}}{\left(x-1\right)\left(x+1\right)x^{2}}$$

ເນື່ອງຈາກ \frac{\left(2x-5\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)x^{2}} ແລະ \frac{3x^{2}}{\left(x-1\right)\left(x+1\right)x^{2}} ມີຕົວຫານດຽວກັນ, ໃຫ້ເພີ່ມພວກມັນໂດຍການເພີ່ມຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.

$$\frac{\left(2x-5\right)\left(x+1\right)+3x^{2}}{\left(x-1\right)\left(x+1\right)x^{2}}$$

ຄູນໃນເສດສ່ວນ \left(2x-5\right)\left(x+1\right)+3x^{2}.

$$\frac{2x^{2}+2x-5x-5+3x^{2}}{\left(x-1\right)\left(x+1\right)x^{2}}$$

ຮວມຂໍ້ກຳນົດໃນ 2x^{2}+2x-5x-5+3x^{2}.

$$\frac{5x^{2}-3x-5}{\left(x-1\right)\left(x+1\right)x^{2}}$$

ຂະຫຍາຍ \left(x-1\right)\left(x+1\right)x^{2}.

$$\frac{5x^{2}-3x-5}{x^{4}-x^{2}}$$

ບອກຄວາມແຕກຕ່າງ w.r.t. x

$$\frac{-10x^{4}+9x^{3}+20x^{2}-3x-10}{x^{3}\left(x^{2}-1\right)^{2}}$$