ປະເມີນ
3+y+3x-xy
ຂະຫຍາຍ
3+y+3x-xy
ແບ່ງປັນ
ສໍາເນົາຄລິບ
\left(\frac{3x\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}-\frac{yx\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\right)\times \frac{x^{2}-1}{x}
ເພື່ອເພີ່ມ ຫຼື ຫານນິພົດ, ໃຫ້ຂະຫຍາຍພວກມັນເພື່ອໃຫ້ຕົວຄູນມີຈຳນວນດຽວກັນ. ຈຳນວນຄູນທີ່ນິຍົມໜ້ອຍທີ່ສຸດຂອງ x-1 ກັບ x+1 ແມ່ນ \left(x-1\right)\left(x+1\right). ຄູນ \frac{3x}{x-1} ໃຫ້ກັບ \frac{x+1}{x+1}. ຄູນ \frac{yx}{x+1} ໃຫ້ກັບ \frac{x-1}{x-1}.
\frac{3x\left(x+1\right)-yx\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\times \frac{x^{2}-1}{x}
ເນື່ອງຈາກ \frac{3x\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} ແລະ \frac{yx\left(x-1\right)}{\left(x-1\right)\left(x+1\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ຫານພວກມັນໂດຍການຫານຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.
\frac{3x^{2}+3x-yx^{2}+yx}{\left(x-1\right)\left(x+1\right)}\times \frac{x^{2}-1}{x}
ຄູນໃນເສດສ່ວນ 3x\left(x+1\right)-yx\left(x-1\right).
\frac{\left(3x^{2}+3x-yx^{2}+yx\right)\left(x^{2}-1\right)}{\left(x-1\right)\left(x+1\right)x}
ຄູນ \frac{3x^{2}+3x-yx^{2}+yx}{\left(x-1\right)\left(x+1\right)} ກັບ \frac{x^{2}-1}{x} ໂດຍການຄູນຕົວເສດຄູນຕົວເສດ ແລະ ຕົວຫານຄູນຫານ.
\frac{x\left(x-1\right)\left(x+1\right)\left(-xy+3x+y+3\right)}{x\left(x-1\right)\left(x+1\right)}
ປັດໃຈທີ່ນິພົດບໍ່ໄດ້ສ້າງເທື່ອ.
-xy+3x+y+3
ຍົກເລີກ x\left(x-1\right)\left(x+1\right) ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.
\left(\frac{3x\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}-\frac{yx\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\right)\times \frac{x^{2}-1}{x}
ເພື່ອເພີ່ມ ຫຼື ຫານນິພົດ, ໃຫ້ຂະຫຍາຍພວກມັນເພື່ອໃຫ້ຕົວຄູນມີຈຳນວນດຽວກັນ. ຈຳນວນຄູນທີ່ນິຍົມໜ້ອຍທີ່ສຸດຂອງ x-1 ກັບ x+1 ແມ່ນ \left(x-1\right)\left(x+1\right). ຄູນ \frac{3x}{x-1} ໃຫ້ກັບ \frac{x+1}{x+1}. ຄູນ \frac{yx}{x+1} ໃຫ້ກັບ \frac{x-1}{x-1}.
\frac{3x\left(x+1\right)-yx\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\times \frac{x^{2}-1}{x}
ເນື່ອງຈາກ \frac{3x\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} ແລະ \frac{yx\left(x-1\right)}{\left(x-1\right)\left(x+1\right)} ມີຕົວຫານດຽວກັນ, ໃຫ້ຫານພວກມັນໂດຍການຫານຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.
\frac{3x^{2}+3x-yx^{2}+yx}{\left(x-1\right)\left(x+1\right)}\times \frac{x^{2}-1}{x}
ຄູນໃນເສດສ່ວນ 3x\left(x+1\right)-yx\left(x-1\right).
\frac{\left(3x^{2}+3x-yx^{2}+yx\right)\left(x^{2}-1\right)}{\left(x-1\right)\left(x+1\right)x}
ຄູນ \frac{3x^{2}+3x-yx^{2}+yx}{\left(x-1\right)\left(x+1\right)} ກັບ \frac{x^{2}-1}{x} ໂດຍການຄູນຕົວເສດຄູນຕົວເສດ ແລະ ຕົວຫານຄູນຫານ.
\frac{x\left(x-1\right)\left(x+1\right)\left(-xy+3x+y+3\right)}{x\left(x-1\right)\left(x+1\right)}
ປັດໃຈທີ່ນິພົດບໍ່ໄດ້ສ້າງເທື່ອ.
-xy+3x+y+3
ຍົກເລີກ x\left(x-1\right)\left(x+1\right) ທັງໃນຕົວເສດ ແລະ ຕົວຫານ.
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}