Rút gọn : \(\frac{x^2+2x-3}{x^2+3x-10}:\frac{x^2+x-6}{x^2-9x+14}:\frac{x^2-4x+3}{x^2+7x+10}\)
Những câu hỏi liên quan
a)Rút gọn \(A=\dfrac{x^2+2x-3}{x^2+3x-10}:\dfrac{x^2+x-6}{x^2-9x+14}.\dfrac{x^2-4x+3}{x^2+7x+10}\)
b) Tìm x để kết quả rút gọn của A > 0; A < 0; A = 0
Rút gọn A : \(\left[\frac{\left(x-1\right)^2}{3x+\left(x-1\right)^2}-\frac{1-2x^2+4x}{x^3-1}+\frac{1}{x-1}\right]:\frac{2x}{x^3+x}\)
\(A=\left(\dfrac{x^2-2x+1}{x^2+x+1}-\dfrac{-2x^2+4x+1}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{1}{x-1}\right):\dfrac{2x}{x^3+x}\)
\(=\dfrac{x^3-3x^2+3x-1+2x^2-4x-1+x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}\cdot\dfrac{x^2+1}{2}\)
\(=\dfrac{x^3-1}{\left(x-1\right)\left(x^2+x+1\right)}\cdot\dfrac{x^2+1}{2}=\dfrac{x^2+1}{2}\)
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1) Rút gọn: a-A=a-2+3-2a-5+a
A=?
2) A=\(\frac{4x^2-3x+17}{x^3-1}+\frac{2x-1}{x^2+x+1}+\frac{6}{1-x}\)
Rút gọn : \(\left[\left(x^3-1-\frac{7-x^3}{3+x^3}\right).\frac{4}{x^5+3x^2}\right]:\left[\frac{3x^6-12}{x^9+6x^6+9x^3}.\frac{x}{3x^3+6}\right]\)
Rút gọn : \(\frac{x}{x-3}-\frac{x^2+3x}{2x+3}.\left(\frac{x+3}{x^2-3x}-\frac{x}{x^2-9}\right)\)
\(=\dfrac{x}{x-3}-\dfrac{x\left(x+3\right)}{2x+3}\cdot\left(\dfrac{x+3}{x\left(x-3\right)}-\dfrac{x}{\left(x+3\right)\left(x-3\right)}\right)\)
\(=\dfrac{x}{x-3}-\dfrac{x\left(x+3\right)}{2x+3}\cdot\dfrac{x^2+6x+9-x^2}{x\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{x}{x-3}-\dfrac{6x+9}{2x+3}\cdot\dfrac{1}{x-3}\)
\(=\dfrac{x-3}{x-3}=1\)
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Giải các bất phương trình sau:
a) frac{x^2-9x+14}{x^2+9x+14}ge0
b) frac{x^2+1}{x^2+3x-10} 0
c) frac{10-x}{5+x^2}frac{1}{2}
d) frac{x+1}{x-1}+2frac{x-1}{x}
e) frac{1}{x+1}+frac{2}{x+3}lefrac{3}{x+2}
f) frac{x-3}{x+1}-frac{x-2}{x-1}lefrac{x^2+4x+15}{x^2-1}
g) frac{x^2-4x+3}{x^2-2x}ge0
h) frac{x+2}{3x+1}lefrac{x-2}{2x-1}
i) frac{11x^2-5x+6}{x^2+5x+6}le x
j) frac{left(1-2xright)left(sqrt{3}x+1right)}{2sqrt{2}x-1}ge0
k) frac{left(5x+1right)-left(7x-2right)}{left(-x^2-1right)left(x^2-4x+...
Đọc tiếp
Giải các bất phương trình sau:
a) \(\frac{x^2-9x+14}{x^2+9x+14}\ge0\)
b) \(\frac{x^2+1}{x^2+3x-10}< 0\)
c) \(\frac{10-x}{5+x^2}>\frac{1}{2}\)
d) \(\frac{x+1}{x-1}+2>\frac{x-1}{x}\)
e) \(\frac{1}{x+1}+\frac{2}{x+3}\le\frac{3}{x+2}\)
f) \(\frac{x-3}{x+1}-\frac{x-2}{x-1}\le\frac{x^2+4x+15}{x^2-1}\)
g) \(\frac{x^2-4x+3}{x^2-2x}\ge0\)
h) \(\frac{x+2}{3x+1}\le\frac{x-2}{2x-1}\)
i) \(\frac{11x^2-5x+6}{x^2+5x+6}\le x\)
j) \(\frac{\left(1-2x\right)\left(\sqrt{3}x+1\right)}{2\sqrt{2}x-1}\ge0\)
k) \(\frac{\left(5x+1\right)-\left(7x-2\right)}{\left(-x^2-1\right)\left(x^2-4x+4\right)}\le0\)
l) \(\frac{1}{x^2-7x+5}\ge\frac{1}{x^2+2x+5}\)
m) \(\frac{\left(x-1\right)\left(x^3-1\right)}{x^2+\left(1+2\sqrt{2}\right)x+2+\sqrt{2}}\le0\)
Giúp mình hoàn thành các bài tập này với ạ.Cảm ơn rất nhìuuuuuuu @@@
@Akai Haruma
Rút gọn : \(\frac{2+x}{2-x}\div\frac{4x^2}{4-4x+x^2}.\left(\frac{2}{2-x}-\frac{8}{8+x^3}.\frac{4-2x+x^2}{2-x}\right)\)
\(\frac{2+x}{2-x}\div\frac{4x^2}{4-4x+x^2}\times\left(\frac{2}{2-x}-\frac{8}{8+x^3}\times\frac{4-2x+x^2}{2-x}\right)\)
\(=\frac{2+x}{2-x}\times\frac{4-4x+x^2}{4x^2}\times\left(\frac{2}{2-x}-\frac{8}{\left(2+x\right)\left(4-2x+x^2\right)}\times\frac{4-2x+x^2}{2-x}\right)\)
\(=\frac{2+x}{2-x}\times\frac{\left(2-x\right)^2}{4x^2}\times\left(\frac{2\left(2+x\right)}{\left(2+x\right)\left(2+x\right)}-\frac{8}{\left(2+x\right)\left(2-x\right)}\right)\)
\(=\frac{\left(2+x\right)\left(2-x\right)}{4x^2}\times\frac{4+2x-8}{\left(2+x\right)\left(2-x\right)}\)
\(=\frac{2\left(2+x-4\right)}{4x^2}\)
\(=\frac{x-2}{2x^2}\)
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Rút gọn C = \(\frac{x}{x-3}-\frac{x^2+3x}{2x+3}.\left(\frac{x+3}{x^2-3x}-\frac{x}{x^2-9}\right)\)
\(C=\frac{x}{x-3}-\frac{x^2+3x}{2x+3}\left(\frac{x+3}{x^2-3x}-\frac{x}{x^2-9}\right)\)
=>\(C=\frac{x}{x-3}-\frac{x\left(x+3\right)}{2x+3}.\left[\frac{x+3}{x\left(x-3\right)}-\frac{x}{\left(x-3\right)\left(x+3\right)}\right]\)
=>\(C=\frac{x}{x-3}-\frac{x\left(x+3\right)}{2x+3}\left[\frac{\left(x+3\right)^2}{x\left(x-3\right)\left(x+3\right)}-\frac{x^2}{x\left(x-3\right)\left(x+3\right)}\right]\)
=>\(C=\frac{x}{x-3}-\frac{x\left(x+3\right)}{2x+3}.\frac{\left(x+3\right)^2-x^2}{x\left(x-3\right)\left(x+3\right)}\)
=>\(C=\frac{x}{x-3}-\frac{x\left(x+3\right)}{2x+3}.\frac{\left(x+3-x\right)\left(x+3+x\right)}{x\left(x-3\right)\left(x+3\right)}\)
=>\(C=\frac{x}{x-3}-\frac{x\left(x+3\right)}{2x+3}.\frac{3\left(2x+3\right)}{x\left(x-3\right)\left(x+3\right)}\)
=>\(C=\frac{x}{x-3}-\frac{3}{x-3}\)
=>\(C=\frac{x-3}{x-3}\)
=>C=1
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a) \(\frac{5-2x}{3}+\frac{\left(x-1\right)\left(x+1\right)}{3x+2}=\frac{\left(x+2\right)\left(1-3x\right)}{9x+6}\)
b)\(1-\frac{x-8}{4x^2-9}=\frac{2}{2x+3}\)
c)\(\frac{-x}{x-10}-\frac{8}{x-6}=\frac{4x}{x^2-16x+60}-1\)
d)\(\frac{7}{x^2-1}+\frac{8}{x^2-2x+1}=\frac{37-9x}{x^3-x^2-x+1}\)
Mình đang cần gấp tks all !