Cho \(P=\left(\dfrac{1}{ax-2}+\dfrac{1}{ax+2}+\dfrac{2ax}{a^2x^2+4}+\dfrac{4a^3x^3}{a^4x^4+16}\right).\dfrac{a^4x^4+16}{a^4x^4}\)
a. Rút gọn
b. tìm P biết \(\dfrac{a^2+4}{x^2+9}=\dfrac{a^2}{9}\)
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Cho \(P=\left(\dfrac{1}{ax-2}+\dfrac{1}{ax+2}+\dfrac{2ax}{a^2x^2+4}+\dfrac{4a^3x^3}{a^4x^4}\right).\dfrac{a^4x^4+16}{a^4x^4}\)
Rút gọn P
\(P=\left(\dfrac{1}{ax-2}+\dfrac{1}{ax+2}+\dfrac{2ax}{a^2x^2+4}+\dfrac{4a^3x^3}{a^2x^4}\right)\cdot\dfrac{a^4x^4+16}{a^4x^4}\)
\(=\left(\dfrac{ax+2+ax-2}{a^2x^2-4}+\dfrac{2ax}{a^2x^2+4}+\dfrac{4a^3x^3}{a^4x^4}\right)\cdot\dfrac{a^4x^4+16}{a^4x^4}\)
\(=\left(\dfrac{2ax\left(a^2x^2+4\right)+2ax\left(a^2x^2-4\right)}{a^4x^4-16}+\dfrac{4a^3x^3}{a^4x^4}\right)\cdot\dfrac{a^4x^4+16}{a^4x^4}\)
\(=\left(\dfrac{4a^3x^3}{a^4x^4-16}+\dfrac{4a^3x^3}{a^4x^4}\right)\cdot\dfrac{a^4x^4+16}{a^4x^4}\)
\(=\dfrac{8a^7x^7-64a^3x^3}{a^4x^4\left(a^4x^4-16\right)}\cdot\dfrac{a^4x^4+16}{a^4x^4}=\dfrac{\left(8a^7x^7-64a^3x^3\right)\left(a^4x^4+16\right)}{a^8x^8\left(a^4x^4-16\right)}\)
\(=\dfrac{8a^3x^3\left(a^4x^4-8\right)\left(a^4x^4+16\right)}{a^8x^8\left(a^4x^4-16\right)}=\dfrac{8\left(a^4x^4-8\right)\left(a^4x^4+16\right)}{a^5x^5\left(a^4x^4-16\right)}\)
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23 tháng 12 2021 lúc 15:35
\(A=\left(\dfrac{4x}{x+2}-\dfrac{x^3-8}{x^3+8}\times\dfrac{4x^2-8x+16}{x^2-4}\right)\div\dfrac{16}{x+2}\times\dfrac{x^2+3x+2}{x^2+x+1}\)
\(B=\dfrac{x^2+x-2}{x^3-1}\)
a) Tìm ĐKXĐ của A, B. Rút gọn A, B
b)Tìm GTLN của A+B
Cho hai biểu thức: A=\(\dfrac{4x-16}{x^2-16}\)và B=\(\dfrac{1}{x}+\dfrac{1}{x+4}+\dfrac{2x-4}{x\left(x+4\right)}\)
a) Rút gọn biểu thức A;
b) Chứng minh: B = A.
\(a,A=\dfrac{4\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}=\dfrac{4}{x+4}\\ b,B=\dfrac{x+4+x+2x-4}{x\left(x+4\right)}=\dfrac{4x}{x\left(x+4\right)}=\dfrac{4}{x+4}=A\)
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Rút gọn:
\(A=\dfrac{2}{x-1}\sqrt{\dfrac{x^2-2x+1}{4x^2}}\)
\(B=\left(x^2-4\right)\sqrt{\dfrac{9}{x^2-4x+4}}\)
\(A=\dfrac{2}{x-1}\sqrt{\dfrac{\left(x-1\right)^2}{4x^2}}=\dfrac{2}{x-1}\left|\dfrac{x-1}{2x}\right|=\dfrac{\left|x-1\right|}{\left(x-1\right)\left|x\right|}\)
\(B=\left(x^2-4\right)\sqrt{\dfrac{9}{x^2-4x+4}}=\dfrac{3\left(x^2-4\right)}{\left|x-2\right|}\)
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a) Ta có: \(A=\dfrac{2}{x-1}\cdot\sqrt{\dfrac{x^2-2x+1}{4x^2}}\)
\(=\dfrac{2}{x-1}\cdot\dfrac{x-1}{2x}\)
\(=\dfrac{1}{x}\)
b) Ta có: \(\left(x^2-4\right)\cdot\sqrt{\dfrac{9}{x^2-4x+4}}\)
\(=\dfrac{\left(x-2\right)\left(x+2\right)\cdot3}{\left(x-2\right)^2}\)
\(=\dfrac{3x+6}{x-2}\)
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23 tháng 12 2021 lúc 13:25
A=\(\left(\dfrac{x-1}{x^2-2x}+\dfrac{x+1}{x^2+2x}-\dfrac{4}{x^3-4x}\right)\div\dfrac{2x+4}{x^2-3x}\)
Rút gọn A
\(A=\left(\dfrac{x-1}{x\left(x-2\right)}+\dfrac{x+1}{x\left(x+2\right)}-\dfrac{4}{x\left(x-2\right)\left(x+2\right)}\right)\cdot\dfrac{x\left(x-3\right)}{2\left(x+2\right)}\)
\(=\dfrac{x^2+x-2+x^2-x+2-4}{x\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x\left(x-3\right)}{2\left(x+2\right)}\)
\(=\dfrac{2x^2-4}{x\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x\left(x-3\right)}{2\left(x+2\right)}\)
\(=\dfrac{2x\left(x^2-2\right)\left(x-3\right)}{2x\left(x-2\right)\cdot\left(x+2\right)^2}=\dfrac{\left(x^2-2\right)\left(x-3\right)}{\left(x-2\right)\left(x+2\right)^2}\)
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Cho biểu thức A = \(\left(\dfrac{4x}{x+2}-\dfrac{x^3-8}{x^3+8}.\dfrac{4x^2-8x+16}{x^2-4}\right):\dfrac{16}{x^2-x-6}\)
a) Rút gọn A
b) Tìm x để A < 0
c) Tìm x để A ≥ 5
a) \(\dfrac{x+3}{x-3}-\dfrac{x-3}{x+3}=\dfrac{36}{x^2-9}\)
b) \(\dfrac{2x-1}{x+4}-\dfrac{1-3x}{x-4}=5+\dfrac{96}{x^2-16}\)
c) \(\dfrac{x+3}{x+1}-\dfrac{x-1}{x}=\dfrac{3x^2+4x+1}{x\left(x+1\right)}\)
P=(1/ax-2 + 1/ax+2 +2ax/a^2x^2+4 + 4a^3x^3/a^4x^4+16) a^4x^4+16/a^4x^4
Rút gọn P
Tính P biết a^2+4/x^2=a^2/9
Không ai trả lời luôn
Rút gọn biểu thức. Chứng minh rằng biểu thức rút gọn không âm vs mọi giá trị của biến thuộc tập xác định (coi a là hằng):
1 - (\(\dfrac{a+x}{ax-x^2}\) + \(\dfrac{2a+3x}{x^2-a^2}\)) : \(\dfrac{a^4-4x^4}{a^4x-a^2x^3}\)