Rút gọn biểu thức: \(D=3.\left(\frac{1}{3}x+1\right)-6.\left|\frac{1}{3}x-2\right|\)
Những câu hỏi liên quan
Rút gọn biểu thức \(B=\left(\left(x+\frac{1}{x}\right)^6-\left(x^6+\frac{1}{x^6}\right)-2\right):\left(\left(x+\frac{1}{x}\right)^3+x^3+\frac{1}{x^3}\right)\)
Rút gọn các biểu thức sau:
\(D=\left(\frac{5\sqrt{x-6}}{x-9}-\frac{2}{\sqrt{x}+3}\right):\left(1+\frac{6}{x-9}\right)\)
\(E=\left(\frac{\sqrt{x}}{3+\sqrt{x}}+\frac{9+x}{9-x}\right).\left(3\sqrt{x}-x\right)\)
rút gọn biểu thức
\(B=\frac{\left(x+\frac{1}{x}\right)^6-\left(x^6+\frac{1}{x^6}\right)-2}{\left(x+\frac{1}{x}\right)^3+x^3+\frac{1}{x^3}}\)
B=\(\frac{3\left(2x^8+5x^6+6x^4+5x^2+2\right)}{x\left(x^2+1\right)\left(2x^4+x^2+2\right)}\)
Rút gọn biểu thức sau: A=\(\left[\left(x^4-x+\frac{x-3}{x^3+1}\right).\frac{\left(x^3-2x^2+2x-1\right)\left(x+1\right)}{x^9+x^7-3x^2-3}+1-\frac{2\left(x+6\right)}{x^2+1}\right].\frac{4x^2+4x+1}{\left(x+4\right)\left(3-x\right)}\)
cho biểu thức:
Q=\(\frac{\left(x+\frac{1}{x}\right)^3-\left(x^6+\frac{1}{x^6}\right)-2}{\left(x+\frac{1}{x}\right)^3+x^3+\frac{1}{x^3}}\)
a)rút gọn Q
b)tìm giá trị nhỏ nhất của Q
1. Cho biểu thức :
\(A=\left[\frac{x+3}{\left(x-3\right)^2}+\frac{6}{x^2-9}-\frac{x-3}{\left(x+3\right)^2}\right].\left[1:\left(\frac{24x^2}{x^4-81}-\frac{12}{x^2+9}\right)\right]\)
a) Rút gọn biểu thức A
b) Tìm x để A=1
c) Tinh giá trị của A khi x = \(\frac{-1}{3}\)
d) Tìm x để A> 0 ; A<0
Rút gọn biểu thức sau:
\(C=\left(\frac{x}{x+3\sqrt{x}}+\frac{1}{\sqrt{x}+3}\right):\left(1-\frac{2}{\sqrt{x}}+\frac{6}{x+3\sqrt{x}}\right)\)
\(C=\left(\frac{x}{x+3\sqrt{x}}+\frac{1}{\sqrt{x}+3}\right):\left(1-\frac{2}{\sqrt{x}}+\frac{6}{x+3\sqrt{x}}\right)\)
\(=\left(\frac{x}{\sqrt{x}\left(\sqrt{x}+3\right)}+\frac{1}{\sqrt{x}+3}\right):\left(1-\frac{2}{\sqrt{x}}+\frac{6}{\sqrt{x}\left(\sqrt{x}+3\right)}\right)\)
\(=\frac{x+1.\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+3\right)}:\frac{\sqrt{x}\left(\sqrt{x}+3\right)-2\left(\sqrt{x}+3\right)+6}{\sqrt{x}\left(\sqrt{x}+3\right)}\)
\(=\frac{x+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+3\right)}:\frac{x+3\sqrt{x}-2\sqrt{x}-6+6}{\sqrt{x}\left(\sqrt{x}+3\right)}\)
\(=\frac{x+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+3\right)}.\frac{\sqrt{x}\left(\sqrt{x}+3\right)}{x+\sqrt{x}}=1\)
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Rút gọn biểu thức sau:\(\left(\frac{1}{x}+1-\frac{3}{x^3+1}+\frac{3}{x^2-x+1}\right).\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2x-2}{x^2+2x}\)
\(\left(\frac{1}{x}+1-\frac{3}{x^3+1}-\frac{3}{x^2-x+1}\right)\cdot\frac{3x^2-3x+3}{\left(x+1\right).\left(x+2\right)}-\frac{2x-2}{x^2+2x}\)
\(=\left(\frac{x+1}{x}-\frac{3}{\left(x+1\right).\left(x^2-x+1\right)}+\frac{3.\left(x+1\right)}{\left(x+1\right).\left(x^2-x+1\right)}\right)\cdot\frac{3.\left(x^2-x+1\right)}{\left(x+1\right).\left(x+2\right)}-\frac{2.\left(x-1\right)}{x.\left(x+2\right)}\)
\(=\left[\frac{\left(x+1\right)^2.\left(x^2-x+1\right)-3x+3x^2+3x}{x.\left(x+1\right).\left(x^2-x+1\right)}\right]\cdot\frac{3.\left(x^2-x+1\right)}{\left(x+1\right).\left(x+2\right)}-\frac{2.\left(x-1\right)}{x.\left(x+2\right)}\)
\(=\left[\frac{x^4+x^3+x+1+3x^2}{x.\left(x+1\right).\left(x^2-x+1\right)}\right]\cdot\frac{3.\left(x^2-x+1\right)}{\left(x+1\right).\left(x+2\right)}-\frac{2.\left(x-1\right)}{x.\left(x+2\right)}\)
\(=\frac{3x^4+3x^3+3x+3+9x^2}{x.\left(x+1\right)^2.\left(x+2\right)}-\frac{2.\left(x-1\right)}{x.\left(x+2\right)}=\frac{3x^4+3x^3+3x+3+9x^2}{x.\left(x+1\right)^2.\left(x+2\right)}-\frac{2x^3+2x^2-2x-2}{x.\left(x+1\right)^2.\left(x+2\right)}\)
\(=\frac{3x^4+x^3+7x^2+5x+5}{x.\left(x+1\right)^2.\left(x+2\right)}\)
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rút gọn biểu thức
\(\left(\frac{1}{x+1}-\frac{3}{x^3+1}+\frac{3}{x^2-x+1}\right):\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2x-2}{x^2+2x}\)
\(\left(\frac{1}{x+1}-\frac{3}{x^3+1}+\frac{3}{x^2-x+1}\right):\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2x-2}{x^2+2x}\left(x\ne-1;x\ne0;x\ne-2\right)\)
\(=\left(\frac{1}{x+1}-\frac{3}{\left(x+1\right)\left(x^2-x+1\right)}+\frac{3}{x^2-x+1}\right):\frac{3x^3-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\left(\frac{x^2-x+1}{\left(x+1\right)\left(x^2-x+1\right)}-\frac{3}{\left(x+1\right)\left(x^2-x+1\right)}+\frac{3x+3}{\left(x+1\right)\left(x^2-x+1\right)}\right)\)\(:\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{x^2-x+1-3+3x+3}{\left(x+1\right)\left(x^2-x+1\right)}:\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{x^2+2x+1}{\left(x+1\right)\left(x^2-x+1\right)}:\frac{3\left(x^2-x+1\right)}{\left(x+1\right)\left(x+1\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x^2-x+1\right)}\cdot\frac{\left(x+1\right)\left(x+2\right)}{3\left(x^2-x+1\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{\left(x+2\right)^2\left(x+1\right)}{3\left(x^2-x+1\right)^2}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(\frac{1}{\left(x+1\right)\left(x+2\right)}-\frac{2}{\left(x+2\right)^2}+\frac{1}{\left(x+2\right)\left(x+3\right)}\)rút gọn biểu thức trên
Xem chi tiết
\(\frac{1}{\left(x+1\right)\left(x+2\right)}-\frac{2}{\left(x+2\right)^2}+\frac{1}{\left(x+2\right)\left(x+3\right)}\)
\(=\frac{\left(x+2\right)\left(x+3\right)-2\left(x+1\right)\left(x+3\right)+\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
\(=\frac{\left(x+3\right)\left(x+2-2x-2\right)+x^2+2x+x+2}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
\(=\frac{\left(x+3\right)\left(-x\right)+x^2+3x+2}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
\(=\frac{-x^2-3x+x^2+3x+2}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}=\frac{2}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
ĐKXD: x\(\ne\)-1,-2,-3
Ta có
\(\frac{1}{\left(x+1\right)\left(x+2\right)}\)-\(\frac{2}{\left(x+2\right)^2}\)+\(\frac{1}{\left(x+2\right)\left(x+3\right)}\)
=\(\frac{\left(x+2\right)\left(x+3\right)-2\left(x+1\right)\left(x+3\right)+\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
=\(\frac{\left(x+2\right)\left(x+3+x+1\right)-2\left(x^2+4x+3\right)}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
=\(\frac{\left(x+2\right)\left(2x+4\right)-2x^2-8x-6}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
=\(\frac{2x^2+8x+8-2x^2-8x-6}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
=\(\frac{2}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
Chúc bạn học tốt
\(ĐKXĐ:\hept{\begin{cases}x\ne-1\\x\ne-2\\x\ne-3\end{cases}}\)
\(\frac{1}{\left(x+1\right)\left(x+2\right)}-\frac{2}{\left(x+2\right)^2}+\frac{1}{\left(x+2\right)\left(x+3\right)}\)
\(=\frac{\left(x+2\right)\left(x+3\right)}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}+\frac{-2\left(x+1\right)\left(x+3\right)}{\left(x+1\right)\left(x+3\right)\left(x+2\right)^2}+\frac{\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+3\right)\left(x+2\right)^2}\)
\(=\frac{\left(x+2\right)\left(x+3\right)-2\left(x+1\right)\left(x+3\right)+\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
\(=\frac{x^2+5x+6-2\left(x^2+4x+3\right)+x^2+3x+2}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)\(=\frac{x^2+5x+6-2x^2-8x-6+x^2+3x+2}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
\(=\frac{2}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)