Rút gọn biểu thức : P = \(\frac{1}{2}-\frac{1}{2}\left(x:\frac{1}{6}-\frac{1}{4}\right)-2\left|3x-2\right|\)
a) \(x\text{ ≥}\frac{2}{3}\) b) \(x< \frac{2}{3}\)
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Ai giải giúp mấy bài toán vsBài 1:Asqrt{frac{1}{text{√}2+1}-frac{text{√}8-text{√}10}{2-text{√}5}}Bfrac{5text{√}5}{text{√}5+2}+frac{text{√}5}{text{√}5-1}-frac{3text{√}5}{3+text{√}5}Bài 2 rút gọn biểu thứcAleft(frac{x+sqrt[]{xy}}{text{√}x+text{√}y}-2right):frac{1}{text{√}x+2} với x :y 0Bleft(frac{a}{a-2text{√}a}+frac{a}{text{√}a-2}right):frac{text{√}a+1}{a-4text{√}a+4}Bài 3 cho biểu thứcPleft(frac{x-2}{x+2text{√}x}+frac{1}{text{√}x+2}right)frac{text{√}x+1}{text{√}x-1}a)Rút gọn Pb)tìm x để Ptext{√}...
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Ai giải giúp mấy bài toán vs
Bài 1:
A=\(\sqrt{\frac{1}{\text{√}2+1}-\frac{\text{√}8-\text{√}10}{2-\text{√}5}}\)
B=\(\frac{5\text{√}5}{\text{√}5+2}+\frac{\text{√}5}{\text{√}5-1}-\frac{3\text{√}5}{3+\text{√}5}\)
Bài 2 rút gọn biểu thức
A=\(\left(\frac{x+\sqrt[]{xy}}{\text{√}x+\text{√}y}-2\right):\frac{1}{\text{√}x+2}\) với x :y >0
B=\(\left(\frac{a}{a-2\text{√}a}+\frac{a}{\text{√}a-2}\right):\frac{\text{√}a+1}{a-4\text{√}a+4}\)
Bài 3 cho biểu thức
P=\(\left(\frac{x-2}{x+2\text{√}x}+\frac{1}{\text{√}x+2}\right)\frac{\text{√}x+1}{\text{√}x-1}\)
a)Rút gọn P
b)tìm x để P=\(\text{√}x+\frac{5}{2}\)
bài 4 rút gọn biểu thức
A=\(\frac{1}{x+\text{√}x}+\frac{2\text{√}x}{x-1}-\frac{1}{x-\text{√}x}\)
B=\(\left(\frac{x}{x+3\text{√}x}+\frac{1}{\text{√}x+3}\right):\left(1-\frac{2}{\text{√}x}+\frac{6}{x+3\text{√}x}\right)\)
Bài 5
A=\(\left(\frac{2}{\text{√}x-3}-\frac{1}{\text{√}x+3}-\frac{x}{\text{√}x\left(x-9\right)}\right):\text{(√}x+3-\frac{x}{\text{√}x-3}\)
a)rút gọn A
b)tìm gtri x để A= -1/4
AI GIẢI GIÙM MÌNH ĐI MÌNH TẠ ƠN
Rút gọn biểu thức sau: A=\(\left[\left(x^4-x+\frac{x-3}{x^3+1}\right).\frac{\left(x^3-2x^2+2x-1\right)\left(x+1\right)}{x^9+x^7-3x^2-3}+1-\frac{2\left(x+6\right)}{x^2+1}\right].\frac{4x^2+4x+1}{\left(x+4\right)\left(3-x\right)}\)
Rút gọn biểu thức
\(A=\left(\frac{x-2}{x+2}-\frac{x+2}{2-x}-\frac{x^2-3x+6}{x^2-4}\right):\left(1-\frac{3}{x-2}\right)\)
\(A=\left(\frac{x-2}{x+2}-\frac{x+2}{2-x}-\frac{x^2-3x+6}{x^2-4}\right):\left(1-\frac{3}{x-2}\right)\)
\(=\left(\frac{\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}+\frac{\left(x+2\right)^2}{\left(x+2\right)\left(x-2\right)}-\frac{x^2-3x+6}{\left(x-2\right)\left(x+2\right)}\right)\)\(:\left(\frac{x-2}{x-2}-\frac{3}{x-2}\right)\)
\(=\frac{x^2-4x+4+x^2+4x+4-x^2+3x-6}{\left(x+2\right)\left(x-2\right)}:\frac{x-2-3}{x-2}\)
\(=\frac{x^2+3x+2}{\left(x+2\right)\left(x-2\right)}:\frac{x-5}{x-2}\)
\(=\frac{x^2+x+2x+2}{\left(x+2\right)\left(x-2\right)}:\frac{x-5}{x-2}\).
\(=\frac{x\left(x+1\right)+2\left(x+1\right)}{\left(x+2\right)\left(x-2\right)}.\frac{x-2}{x-5}\)
\(=\frac{\left(x+2\right)\left(x+1\right)}{\left(x+2\right)\left(x-2\right)}.\frac{x-2}{x-5}\)
\(=\frac{x+1}{x-2}.\frac{x-2}{x-5}\)
\(=\frac{x+1}{x-5}\)
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rút gọn biểu thức
\(\left(\frac{1}{x+1}-\frac{3}{x^3+1}+\frac{3}{x^2-x+1}\right):\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2x-2}{x^2+2x}\)
\(\left(\frac{1}{x+1}-\frac{3}{x^3+1}+\frac{3}{x^2-x+1}\right):\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2x-2}{x^2+2x}\left(x\ne-1;x\ne0;x\ne-2\right)\)
\(=\left(\frac{1}{x+1}-\frac{3}{\left(x+1\right)\left(x^2-x+1\right)}+\frac{3}{x^2-x+1}\right):\frac{3x^3-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\left(\frac{x^2-x+1}{\left(x+1\right)\left(x^2-x+1\right)}-\frac{3}{\left(x+1\right)\left(x^2-x+1\right)}+\frac{3x+3}{\left(x+1\right)\left(x^2-x+1\right)}\right)\)\(:\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{x^2-x+1-3+3x+3}{\left(x+1\right)\left(x^2-x+1\right)}:\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{x^2+2x+1}{\left(x+1\right)\left(x^2-x+1\right)}:\frac{3\left(x^2-x+1\right)}{\left(x+1\right)\left(x+1\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x^2-x+1\right)}\cdot\frac{\left(x+1\right)\left(x+2\right)}{3\left(x^2-x+1\right)}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
\(=\frac{\left(x+2\right)^2\left(x+1\right)}{3\left(x^2-x+1\right)^2}-\frac{2\left(x-1\right)}{x\left(x+2\right)}\)
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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tính(rút gọn)
a,\(\left(x+3-\frac{1}{x+3}\right)\left(x+\frac{3}{x+4}\right)\)
b,\(\left(2x-4-\frac{x-12}{3x+4}\right)\left(3x-2-\frac{10}{2x+1}\right)\)
c,\(\left(2x-8-\frac{x+10}{3x+1}\right)\left(x-6-\frac{x-6}{3x+2}\right)\)
d,\(\left(1+\frac{1}{x}\right):\left(1-\frac{1}{x^2}\right)\)
Cho biểu thức K=\(\left[\frac{x^2}{x^2-5x+6}+\frac{x^2}{x^2-3x+6}\right].\frac{\left(x-1\right)\left(x-3\right)}{x^4+x^2+1}\)
a) tìm điều kiện xác định rồi rút gọn x
b) tìm gtln của K
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 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=\(\frac{3\left(2x^8+5x^6+6x^4+5x^2+2\right)}{x\left(x^2+1\right)\left(2x^4+x^2+2\right)}\)