ແກ້ r+2/r(r+3)-r-1/r(r+2)

$$\frac { r + 2 } { r ( r + 3 ) } - \frac { r - 1 } { r ( r + 2 ) }$$

ປະເມີນ

$$\frac{2r+7}{r\left(r+2\right)\left(r+3\right)}$$

ຂັ້ນຕອນທາງອອກສັ້ນ

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

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

ເນື່ອງຈາກ \frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)} ແລະ \frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ຫານພວກມັນໂດຍການຫານຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.

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

ຄູນໃນເສດສ່ວນ \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

$$\frac{r^{2}+2r+2r+4-r^{2}-3r+r+3}{r\left(r+2\right)\left(r+3\right)}$$

ຮວມຂໍ້ກຳນົດໃນ r^{2}+2r+2r+4-r^{2}-3r+r+3.

$$\frac{2r+7}{r\left(r+2\right)\left(r+3\right)}$$

ຂະຫຍາຍ r\left(r+2\right)\left(r+3\right).

$$\frac{2r+7}{r^{3}+5r^{2}+6r}$$

ຂະຫຍາຍ

$$\frac{2r+7}{r\left(r+2\right)\left(r+3\right)}$$

ຂັ້ນຕອນທາງອອກສັ້ນ

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

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

ເນື່ອງຈາກ \frac{\left(r+2\right)\left(r+2\right)}{r\left(r+2\right)\left(r+3\right)} ແລະ \frac{\left(r-1\right)\left(r+3\right)}{r\left(r+2\right)\left(r+3\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ຫານພວກມັນໂດຍການຫານຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.

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

ຄູນໃນເສດສ່ວນ \left(r+2\right)\left(r+2\right)-\left(r-1\right)\left(r+3\right).

$$\frac{r^{2}+2r+2r+4-r^{2}-3r+r+3}{r\left(r+2\right)\left(r+3\right)}$$

ຮວມຂໍ້ກຳນົດໃນ r^{2}+2r+2r+4-r^{2}-3r+r+3.

$$\frac{2r+7}{r\left(r+2\right)\left(r+3\right)}$$

ຂະຫຍາຍ r\left(r+2\right)\left(r+3\right).

$$\frac{2r+7}{r^{3}+5r^{2}+6r}$$