ແກ້ສຳລັບ x
x<1
Graph
ແບ່ງປັນ
ສໍາເນົາຄລິບ
\frac{x^{2}}{x-1}-x\leq 1
ລົບ x ອອກຈາກທັງສອງຂ້າງ.
\frac{x^{2}}{x-1}-\frac{x\left(x-1\right)}{x-1}\leq 1
ເພື່ອເພີ່ມ ຫຼື ຫານນິພົດ, ໃຫ້ຂະຫຍາຍພວກມັນເພື່ອໃຫ້ຕົວຄູນມີຈຳນວນດຽວກັນ. ຄູນ x ໃຫ້ກັບ \frac{x-1}{x-1}.
\frac{x^{2}-x\left(x-1\right)}{x-1}\leq 1
ເນື່ອງຈາກ \frac{x^{2}}{x-1} ແລະ \frac{x\left(x-1\right)}{x-1} ມີຕົວຫານດຽວກັນ, ໃຫ້ຫານພວກມັນໂດຍການຫານຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.
\frac{x^{2}-x^{2}+x}{x-1}\leq 1
ຄູນໃນເສດສ່ວນ x^{2}-x\left(x-1\right).
\frac{x}{x-1}\leq 1
ຮວມຂໍ້ກຳນົດໃນ x^{2}-x^{2}+x.
x-1>0 x-1<0
Denominator x-1 cannot be zero since division by zero is not defined. There are two cases.
x>1
Consider the case when x-1 is positive. Move -1 to the right hand side.
x\leq x-1
The initial inequality does not change the direction when multiplied by x-1 for x-1>0.
x-x\leq -1
Move the terms containing x to the left hand side and all other terms to the right hand side.
0\leq -1
ຮວມຄຳສັບ.
x\in \emptyset
Consider condition x>1 specified above.
x<1
Now consider the case when x-1 is negative. Move -1 to the right hand side.
x\geq x-1
The initial inequality changes the direction when multiplied by x-1 for x-1<0.
x-x\geq -1
Move the terms containing x to the left hand side and all other terms to the right hand side.
0\geq -1
ຮວມຄຳສັບ.
x<1
Consider condition x<1 specified above.
x<1
ວິທີແກ້ສຸດທ້າຍແມ່ນເປັນການຮວມວິທີການທີ່ຊອກມາໄດ້.
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