ແກ້ f(x)=(x^2+4x+3/x^2+2x-3-x^2+2x+1/x^2+3x+2)*x+2/x+1

$$f ( x ) = ( \frac { x ^ { 2 } + 4 x + 3 } { x ^ { 2 } + 2 x - 3 } - \frac { x ^ { 2 } + 2 x + 1 } { x ^ { 2 } + 3 x + 2 } ) \cdot \frac { x + 2 } { x + 1 }$$

ປະເມີນ

$$\frac{3}{x-1}$$

ຂັ້ນຕອນທາງອອກສັ້ນ

ປັດໃຈທີ່ນິພົດບໍ່ມີຢູ່ໃນ \frac{x^{2}+4x+3}{x^{2}+2x-3}.

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

ຍົກເລີກ x+3 ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.

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

ປັດໃຈທີ່ນິພົດບໍ່ມີຢູ່ໃນ \frac{x^{2}+2x+1}{x^{2}+3x+2}.

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

ຍົກເລີກ x+1 ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.

$$\left(\frac{x+1}{x-1}-\frac{x+1}{x+2}\right)\times \frac{x+2}{x+1}$$

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

$$\left(\frac{\left(x+1\right)\left(x+2\right)}{\left(x-1\right)\left(x+2\right)}-\frac{\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x+2\right)}\right)\times \frac{x+2}{x+1}$$

ເນື່ອງຈາກ \frac{\left(x+1\right)\left(x+2\right)}{\left(x-1\right)\left(x+2\right)} ແລະ \frac{\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x+2\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ຫານພວກມັນໂດຍການຫານຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.

$$\frac{\left(x+1\right)\left(x+2\right)-\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x+2\right)}\times \frac{x+2}{x+1}$$

ຄູນໃນເສດສ່ວນ \left(x+1\right)\left(x+2\right)-\left(x+1\right)\left(x-1\right).

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

ຮວມຂໍ້ກຳນົດໃນ x^{2}+2x+x+2-x^{2}+x-x+1.

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

ຄູນ \frac{3x+3}{\left(x-1\right)\left(x+2\right)} ກັບ \frac{x+2}{x+1} ໂດຍການຄູນຕົວເສດຄູນຕົວເສດ ແລະ ຕົວຫານຄູນຫານ.

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

ຍົກເລີກ x+2 ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.

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

ປັດໃຈທີ່ນິພົດບໍ່ໄດ້ສ້າງເທື່ອ.

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

ຍົກເລີກ x+1 ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.

$$\frac{3}{x-1}$$

ຂະຫຍາຍ

$$\frac{3}{x-1}$$

ຂັ້ນຕອນທາງອອກສັ້ນ

ປັດໃຈທີ່ນິພົດບໍ່ມີຢູ່ໃນ \frac{x^{2}+4x+3}{x^{2}+2x-3}.

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

ຍົກເລີກ x+3 ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.

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

ປັດໃຈທີ່ນິພົດບໍ່ມີຢູ່ໃນ \frac{x^{2}+2x+1}{x^{2}+3x+2}.

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

ຍົກເລີກ x+1 ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.

$$\left(\frac{x+1}{x-1}-\frac{x+1}{x+2}\right)\times \frac{x+2}{x+1}$$

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

$$\left(\frac{\left(x+1\right)\left(x+2\right)}{\left(x-1\right)\left(x+2\right)}-\frac{\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x+2\right)}\right)\times \frac{x+2}{x+1}$$

ເນື່ອງຈາກ \frac{\left(x+1\right)\left(x+2\right)}{\left(x-1\right)\left(x+2\right)} ແລະ \frac{\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x+2\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ຫານພວກມັນໂດຍການຫານຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.

$$\frac{\left(x+1\right)\left(x+2\right)-\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x+2\right)}\times \frac{x+2}{x+1}$$

ຄູນໃນເສດສ່ວນ \left(x+1\right)\left(x+2\right)-\left(x+1\right)\left(x-1\right).

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

ຮວມຂໍ້ກຳນົດໃນ x^{2}+2x+x+2-x^{2}+x-x+1.

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

ຄູນ \frac{3x+3}{\left(x-1\right)\left(x+2\right)} ກັບ \frac{x+2}{x+1} ໂດຍການຄູນຕົວເສດຄູນຕົວເສດ ແລະ ຕົວຫານຄູນຫານ.

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

ຍົກເລີກ x+2 ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.

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

ປັດໃຈທີ່ນິພົດບໍ່ໄດ້ສ້າງເທື່ອ.

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

ຍົກເລີກ x+1 ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.

$$\frac{3}{x-1}$$