Rút gọn bt \(A=\left(\frac{1}{1-x}+\frac{2}{x+1}-\frac{5-x}{1-x^2}\right):\frac{1-2x}{x^2-1}\)
Những câu hỏi liên quan
\(\frac{\left(x+\frac{1}{x}\right)^4-\left(x^4+\frac{1}{x^4}\right)-2}{\left(x+\frac{1}{x}\right)^4+x^2+\frac{1}{x^2}}\cdot\frac{x^4+1999x^2+1}{2x^2}\)
a,Rút gọn bt
b,tính giá trị của bt biết \(x^2-4x+1=0\)
Cho bt sau:A=\(\left(\frac{1}{x-1}-\frac{x}{1-x^3}.\frac{x^2+x+1}{x+1}\right):\frac{2x+1}{x^2+2x+1}\)
a)Rút gọn bt A?
b)Tính giá trị của A khi x=\(\frac{1}{2}\)
Cho bt
\(C=\left(\frac{x^2+x}{x^2-2x+1}\right):\left(\frac{x+1}{x}-\frac{1}{1-x}+\frac{2-x^2}{x^2-x}\right)\)
a, Rút gọn C
b,Tìm x dể B có gt nguyên
làm a thôi nha :D
a) \(C=\left(\frac{x^2+x}{x^2-2x+1}\right):\left(\frac{x+1}{x}-\frac{1}{1-x}+\frac{2-x^2}{x^2-x}\right)\)
\(C=\frac{x\left(x+1\right)}{x^2-2x+1}.\left[\frac{x+1}{x}-\frac{1}{-\left(x-1\right)}+\frac{2-x^2}{x\left(x+1\right)}\right]\)
\(C=\frac{x\left(x+1\right)}{x^2-2x+1}.\left[\frac{x+1}{x}+\frac{1}{x-1}+\frac{2-x^2}{x\left(x-1\right)}\right]\)
\(C=\frac{x\left(x+1\right)}{x^2-2x+1}.\left[\frac{x+1}{x}+\frac{x+2-x^2}{x\left(x-1\right)}\right]\)
\(C=\frac{x\left(x+1\right)}{x^2-2x+1}.\left[\frac{\left(x-1\right)\left(x+1\right)+x+2-x^2}{x\left(x-1\right)}\right]\)
\(C=\frac{x+1}{x^2-2x+1}.\frac{x^2-1+x+2-x^2}{x-1}\)
\(C=\frac{x+1}{\left(x^2-2x+1\right)}.\frac{1.x}{x-1}\)
\(C=\frac{\left(x+1\right)^2}{x^3-x^2-2x^2+2x+x-1}\)
\(C=\frac{x^2+2x+1}{x^3-3x^2+3x-1}\)
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a)\(C=\left[\frac{x.\left(x+1\right)}{\left(x-1\right)^2}\right]:\left[\frac{x+1}{x}-\frac{1}{-\left(x-1\right)}+\frac{-x^2+2}{x.\left(x-1\right)}\right]\)
\(C=\left[\frac{x.\left(x+1\right)}{\left(x-1\right)^2}\right]:\left[\frac{x^2-1}{x.\left(x-1\right)}+\frac{x}{x.\left(x-1\right)}+\frac{-x^2+2}{x.\left(x-1\right)}\right]\)
\(C=\left[\frac{x.\left(x+1\right)}{\left(x-1\right)^2}\right]:\left[\frac{x^2-1+x-x^2+2}{x.\left(x-1\right)}\right]\)
\(C=\left[\frac{x.\left(x+1\right)}{\left(x-1\right)^2}\right]:\left[\frac{x+1}{x.\left(x-1\right)}\right]=\left[\frac{x.\left(x+1\right)}{\left(x-1\right)^2}\right].\left[\frac{x.\left(x-1\right)}{x+1}\right]=\frac{x.\left(x+1\right).x}{\left(x-1\right).\left(x+1\right)}=\frac{x^2}{x-1}\)
b)\(\text{Để B nguyên }\Rightarrow x^2⋮x-1\)
\(x^2=x^2-1+1=\left(x-1\right).\left(x+1\right)+1\)
\(\Rightarrow\text{Để }x^2⋮x-1\Rightarrow1⋮x-1\Rightarrow x-1\inƯ\left(1\right)=\left\{\pm1\right\}\Rightarrow x\in\left\{2;0\right\}\)
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cho bt:
\(A=\left(\frac{x^2+2x}{x^3+2x^2+4x+8}+\frac{2}{x^2+4}\right):\left(\frac{1}{x+2}+\frac{4x}{8-4x+2x^2-x^3}\right)\)
a) Rút gọn bt
b) Tìm giá trị của x để \(A< \frac{1}{5}\)
cho bt \(\left(\frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}\right):\left[1:\left(1-\frac{1}{x}+\frac{1}{4x^2}\right)\right]\)
a, rút gọn bt
b, tính giá trị bt khi X thoả mãn trị tuyệt đối của x + 1 = 3
ai nhanh tick cho nè mấy bạn siêu toán 8
Cho bt \(P=\left(2-\frac{x-1}{2x-3}\right):\left(\frac{6x+1}{2X^2-x-3}+\frac{x}{x+1}\right)\)
a) Rút gọn P
b)So sánh P và \(\frac{3}{2}\)
M =\(\left(\frac{x-2}{2x-2}-\frac{x+3}{2x+2}+\frac{3}{2x-2}\right):\left(1-\frac{x-3}{x+1}\right)\)
a, tìm điều kiện của x để giá trị bt M có giá trị
b, rút gọn M
ai nhanh tik 5 lần nhé <3
a) Phân thức M xác định khi và chỉ khi :
+) \(2x-2\ne0\Leftrightarrow x\ne1\)
+) \(2x+2\ne0\Leftrightarrow x\ne-1\)
+) \(1-\frac{x-3}{x+1}\ne0\)
\(\Leftrightarrow x-3\ne x+1\)
\(\Leftrightarrow0x\ne4\left(\text{luôn đúng}\right)\)
Vậy \(x\ne\left\{1;-1\right\}\)
b) \(M=\left(\frac{x-2}{2x-2}-\frac{x+3}{2x+2}+\frac{3}{2x-2}\right):\left(1-\frac{x-3}{x+1}\right)\)
\(M=\left(\frac{\left(x-2\right)\left(2x+2\right)}{\left(2x-2\right)\left(2x+2\right)}-\frac{\left(x+3\right)\left(2x-2\right)}{\left(2x-2\right)\left(2x+2\right)}+\frac{3\left(2x+2\right)}{\left(2x-2\right)\left(2x+2\right)}\right):\left(\frac{x+1-x+3}{x+1}\right)\)
\(M=\left(\frac{2x^2-2x-4-2x^2-4x+6+6x+6}{\left(2x-2\right)\left(2x+2\right)}\right):\left(\frac{4}{x+1}\right)\)
\(M=\frac{8}{2\left(x-1\right)2\left(x+1\right)}\cdot\frac{x+1}{4}\)
\(M=\frac{8\left(x+1\right)}{4\left(x-1\right)\left(x+1\right)\cdot4}\)
\(M=\frac{8\left(x+1\right)}{8\left(x+1\right)\left(x-1\right)}\)
\(M=\frac{1}{x-1}\)
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\(M=\left(\frac{x-2}{2x-2}-\frac{x+3}{2x+2}+\frac{3}{2x-2}\right):\left(1-\frac{x-3}{x+1}\right)\)
\(=\left(\frac{x+1}{2x-2}-\frac{x+3}{2x+2}\right):\left(\frac{4}{x+1}\right)=\left[\frac{\left(x+1\right)\left(2x+2\right)-\left(x+3\right)\left(2x-2\right)}{\left(2x-2\right)\left(2x+2\right)}\right]:\left(\frac{4}{x+1}\right)\)
\(=\left[\frac{2x^2+4x+2-2x^2+2x+6-6x+6}{4x^2-4}\right]:\left(\frac{4}{x+1}\right)\)
\(=\left[\frac{6x+8-6x+6}{4x^2-4}\right]:\left(\frac{4}{x+1}\right)\)
\(=\frac{14}{4x^2-4}:\left(\frac{4}{x+1}\right)=\frac{14x+14}{16x^2-16}=\frac{7x+7}{8x^2-8}\)
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I,Rút gọn biểu thức chứa dấu GTTĐ
1.A= |x-3,5|+|4,1-x|
2.B= |-x+3,5|+|x-4,1|
II,Rút gon BT khi \(\frac{-3}{5}< x< \frac{1}{7}\)
\(1,A=\left|x-\frac{1}{7}\right|-\left|x+\frac{3}{5}\right|+\frac{4}{5}\)
\(2,B=\left|-x+\frac{1}{7}\right|+\left|-x-\frac{3}{5}\right|-\frac{2}{6}\)
Rút gọn phân thức :
a) \(P=\left(\frac{1}{x-1}-\frac{x}{1-x^3}.\frac{x^2+x+1}{x+1}\right):\frac{2x+1}{x^2+2x+1}\)
b) \(Q=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{50-5x}{2x\left(x+5\right)}\)
P/s : Típ nè :v
a) \(P=\left(\frac{1}{x-1}-\frac{x}{1-x^3}.\frac{x^2+x+1}{x+1}\right):\frac{2x+1}{x^2+2x+1}\)
\(=\left(\frac{1}{x-1}-\frac{x}{\left(1-x\right)\left(1+x+x^2\right)}.\frac{x^2+x+1}{x+1}\right).\frac{x^2+2x+1}{2x+1}\)
\(=\left(\frac{1}{x-1}-\frac{x}{\left(x-1\right)\left(x+1\right)}\right).\frac{x^2+2x+1}{2x+1}\)
\(=\left(\frac{x+1}{\left(x-1\right)\left(x+1\right)}-\frac{x}{\left(x-1\right)\left(x+1\right)}\right).\frac{x^2+2x+1}{2x+1}\)
\(=\frac{1}{\left(x-1\right)\left(x+1\right)}.\frac{\left(x+1\right)^2}{2x+1}\)
\(=\frac{x+1}{\left(x-1\right)\left(2x+1\right)}\)
b) \(Q=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{5x-5x}{2x\left(x+5\right)}\)
\(=\frac{x\left(x^2+2x\right)}{2x\left(x+5\right)}+\frac{2\left(x-5\right)\left(x+5\right)}{2x\left(x+5\right)}+\frac{50-5x}{2x\left(x+5\right)}\)
\(=\frac{x^3+2x^2+2\left(x^2-25\right)+50-5x}{2x\left(x+5\right)}\)
\(=\frac{x^3+2x^2+2x^2-50+50-5x}{2x\left(x+5\right)}\)
\(=\frac{x^3+4x^2-5x}{2x\left(x+5\right)}\)
\(=\frac{x^3-x^2+5x^2-5x}{2x\left(x+5\right)}\)
\(=\frac{x^2\left(x-1\right)+5x\left(x-1\right)}{2x\left(x+5\right)}\)
\(=\frac{\left(x-1\right)\left(x^2+5x\right)}{2x\left(x+5\right)}\)
\(=\frac{x\left(x-1\right)\left(x+5\right)}{2x\left(x+5\right)}\)
\(=\frac{x-1}{2}\)
xin lỗi phần a làm sai mình làm lại
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