Rút gọn biểu thức sau: (x-2)^3+6(x-1)^2-(x+1)(x^2-x+1)
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NQ
1
Y
25 tháng 6 2023
\(A=\left(\dfrac{3x-x^2}{9-x^2}-1\right):\left(\dfrac{9-x^2}{x^2+x-6}+\dfrac{x-3}{2-x}-\dfrac{x+2}{x+3}\right)\left(dk:x\ne\pm3,x\ne2\right)\)
\(=\dfrac{3x-x^2-9+x^2}{9-x^2}:\left(\dfrac{9-x^2}{\left(x-2\right)\left(x+3\right)}-\dfrac{x-3}{x-2}-\dfrac{x+2}{x+3}\right)\)
\(=\dfrac{3x-9}{9-x^2}:\dfrac{9-x^2-\left(x-3\right)\left(x+3\right)-\left(x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x+3\right)}\)
\(=-\dfrac{3\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}.\dfrac{\left(x-2\right)\left(x+3\right)}{9-x^2-\left(x^2-9\right)-\left(x^2-4\right)}\)
\(=-\dfrac{3}{x+3}.\dfrac{\left(x-2\right)\left(x+3\right)}{9-x^2-x^2+9-x^2+4}\)
\(=\dfrac{-3\left(x-2\right)}{22-3x^2}\)
\(=\dfrac{-3x+6}{22-3x^2}\)
Vậy \(A=\dfrac{-3x+6}{22-3x^2}\) với \(x\ne\pm3,x\ne2\)
5 tháng 5 2021
Câu 1:
Sửa đề: \(B=\left(\dfrac{x}{x+3\sqrt{x}}+\dfrac{1}{\sqrt{x}+3}\right):\left(1-\dfrac{2}{\sqrt{x}}+\dfrac{6}{x+3\sqrt{x}}\right)\)
Ta có: \(B=\left(\dfrac{x}{x+3\sqrt{x}}+\dfrac{1}{\sqrt{x}+3}\right):\left(1-\dfrac{2}{\sqrt{x}}+\dfrac{6}{x+3\sqrt{x}}\right)\)
\(=\left(\dfrac{x}{\sqrt{x}\left(\sqrt{x}+3\right)}+\dfrac{1}{\sqrt{x}+3}\right):\left(\dfrac{x+3\sqrt{x}-2\left(\sqrt{x}+3\right)+6}{\sqrt{x}\left(\sqrt{x}+3\right)}\right)\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}+3}:\dfrac{x+3\sqrt{x}-2\sqrt{x}-6+6}{\sqrt{x}\left(\sqrt{x}+3\right)}\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}+3}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}+3\right)}{x+\sqrt{x}}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}=1\)
5 tháng 5 2021
Câu 3:
Ta có: \(Q=\left(\dfrac{a}{a-2\sqrt{a}}+\dfrac{a}{\sqrt{a}-2}\right):\dfrac{\sqrt{a}+1}{a-4\sqrt{a}+4}\)
\(=\left(\dfrac{a}{\sqrt{a}\left(\sqrt{a}-2\right)}+\dfrac{a}{\sqrt{a}-2}\right):\dfrac{\sqrt{a}+1}{\left(\sqrt{a}-2\right)^2}\)
\(=\dfrac{a+\sqrt{a}}{\sqrt{a}-2}\cdot\dfrac{\sqrt{a}-2}{\sqrt{a}+1}\cdot\dfrac{\sqrt{a}-2}{1}\)
\(=\sqrt{a}\left(\sqrt{a}-2\right)\)
\(=a-2\sqrt{a}\)
AT
1
21 tháng 7 2023
\(P=\dfrac{\sqrt{x}}{\sqrt{x}-1}+\dfrac{2}{\sqrt{x}+3}+\dfrac{2-6\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{x+3\sqrt{x}+2\sqrt{x}-2+2-6\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{x-\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}=\dfrac{\sqrt{x}}{\sqrt{x}+3}\)
20 tháng 12 2020
a. \(4x\left(3x-2\right)-3x\left(4x+1\right)\)
\(=12x^2-8x-12x^2-3x\)
\(=-11x\) \(\left(1\right)\)
Thay \(x=-2\) vào \(\left(1\right)\) ta được :
\(-11.\left(-2\right)=22\)
b. \(\left(x+3\right)\left(x-3\right)-\left(x-1\right)^2\)
\(=\left(x^2-9\right)-\left(x^2-2x+1\right)\)
\(=x^2-9-x^2+2x-1\)
\(=2x-10\) \(\left(2\right)\)
Thay \(x=6\) vào \(\left(2\right)\) ta được :
\(2.6-10=2\)
UB
1
23 tháng 7 2021
Ta có: \(A=\left(x-y-1\right)^3-\left(x-y+1\right)^3+6\left(x-y\right)^2\)
\(=\left(x-y-1-x+y-1\right)\left[\left(x-y-1\right)^2+\left(x-y-1\right)\left(x-y+1\right)+\left(x-y+1\right)^2\right]+6\left(x-y\right)^2\)
\(=-2\cdot\left[3\left(x-y\right)^2+1\right]+6\left(x-y\right)^2\)
\(=-6\left(x-y\right)^2+6\left(x-y\right)^2-2\)
=-2
17 tháng 4 2021
\(\left(\dfrac{\dfrac{x}{x+1}}{\dfrac{x^2}{x^2+x+1}}-\dfrac{2x+1}{x^2+x}\right)\dfrac{x^2-1}{x-1}\)ĐK : \(x\ne\pm1\)
\(=\left(\dfrac{x}{x+1}.\dfrac{x^2+x+1}{x^2}-\dfrac{2x+1}{x\left(x+1\right)}\right)\left(x+1\right)=\left(\dfrac{x^2+x-1}{x^2+x}-\dfrac{2x+1}{x\left(x+1\right)}\right)\left(x+1\right)\)
\(=\left(\dfrac{x^2+x-1-2x-1}{x\left(x+1\right)}\right)\left(x+1\right)=\dfrac{x^2-3x-2}{x}\)
17 tháng 4 2021
à xin lỗi mình nhầm dòng cuối
\(=\dfrac{x^2-x-2}{x}=\dfrac{\left(x+1\right)\left(x-2\right)}{x}\)
Để biểu thức trên nhận giá trị dương khi
\(\dfrac{\left(x+1\right)\left(x-2\right)}{x}>0\)bạn tự xét TH cả tử và mẫu nhé, mình đánh trên này bị lỗi
YN
1 tháng 7 2021
\(a)\)
\(\left(2x+3\right)^2+\left(2x-3\right)^2-\left(2x+3\right)\left(4x-6\right)+xy\)
\(=\left(2x+3\right)^2-2\left(2x+3\right)\left(2x-3\right)+\left(2x-3\right)^2+xy\)
\(=\left(2x+3-2x+3\right)^2+xy\)
\(=6^2+2\left(-1\right)\)
\(=36-2\)
\(=34\)
\(b)\)
\(\left(x-2\right)^2-\left(x-1\right)\left(x+1\right)-x\left(1-x\right)\)
\(=x^2-4x+4-x^2+1-x+x^2\)
\(=x^2-5x+5\)
Thay \(x=-2\)vào ta có:
\(\left(-2\right)^2-5\left(-2\right)+5\)
\(=4+10+5\)
\(=19\)
PT
1
CM
30 tháng 3 2018
(x + 2)(x – 2) – (x – 3)(x + 1)
= x2 – 22 – (x2 + x – 3x – 3)
= x2 – 4 – x2 – x + 3x + 3
= 2x – 1
