P=\((\)\(\frac{2x}{2x^2-5x+3}\)- \(\frac{5}{2x-3}\)\()\):\((3+\frac{2}{1-x})\)
a, rút gọn P
b, P=? khi |2x-1|=3
c, x=? để P>1
D, tìm x\(\varepsilon\)Z để P\(\varepsilon\)Z
P=(\(\frac{2x}{2x^2-5x+3}\)-\(\frac{5}{2x-3}\)) : (3+ \(\frac{2}{1-x}\))
a, Rút gọn P
b, P=? khi | 2x- 1|=3
c, x=? để P \(\varepsilon\)Z
d, Tìm x\(\varepsilon\)Z để P\(\varepsilon\)Z
\(P=\left(\frac{2x}{2x^2-5x+2}-\frac{5}{2x-3}\right):\left(3+\frac{2}{1-x}\right) \)(dk x khac 3/2 ; x khac 1)
\(P=\left(\frac{2x}{\left(2x-3\right)\left(x-1\right)}-\frac{5\left(x-1\right)}{\left(2x+3\right)\left(x-1\right)}\right):\left(\frac{3\left(x-1\right)}{x-1}-\frac{2}{x-1}\right)\)
\(P=\frac{2x-5x+5}{\left(2x-3\right)\left(x-1\right)}:\frac{3x-3-2}{x-1}\)
\(P=\frac{-\left(3x-5\right)}{\left(2x-3\right)\left(x-1\right)}\cdot\frac{x-1}{3x-5}\)
\(P=\frac{-1}{2x-3}\)
b) TC: \(|2x-1|=3\)
TH1) \(|2x-1|=2x-1\)khi \(x\ge\frac{1}{2}\)
2x-1=3 suy ra x=2 ( thoa dk)
TH2) \(|2x-1|=-2x+1\)khi \(x< \frac{1}{2}\)
-2x+1=3 suy ra x=-1 ( thoa dk)
khi x= 2 thi P=-1
khi x= -1 thi P=1/5
c) de P thuoc Z thi \(-\frac{1}{2x-3}\)thuoc Z
suy ra \(\frac{1}{3-2x}\)thuoc Z
suy ra 3-2x thuoc \(Ư\left(1\right)\in\left\{\pm1\right\}\)
khi 3-2x=1 thi x= 1 (ko thoa dk x khac 1)
khi 3-2x=-1 thi x=2(thoa dk)
vay x=2 thi P thuoc Z
d) giai tg tu cau c
P= (\(\frac{2x}{2x^2-5x+3}\)_ \(\frac{5}{2x-3}\)) :(3+ \(\frac{2}{1-x}\))
a, Rút gọn P
b, P=? để P>1
d, Tìm x\(\varepsilon\)Z để P\(\varepsilon\)Z
A=( 1+\(\frac{x^2}{x^2+1}\)) :( \(\frac{1}{x-1}-\frac{2x}{x^3+x-x^2-1}\))
a, rút gọn A
b, A=? khi x= \(\frac{-1}{2}\)
c, x=? để A<1
d, Tìm x\(\varepsilon\)Z để A \(\varepsilon\)Z
A=\((1+\frac{x^2}{x^2+1})\): \((\frac{1}{x-1}-\frac{2x}{x^3+x-x^2-1})\)
a, Rút gọn A
b, A=? khi x=\(\frac{-1}{2}\)
c, x=? đểA<1
d, Tìm x\(\varepsilon\)Z để A \(\varepsilon Z\)
A= (1+\(\frac{x^2}{X^2+1}\)) : (\(\frac{1}{x-1}\)- \(\frac{2x}{x^3+x-x^2-1}\))
a, Rút gọn A
b, A=? khi x= \(\frac{-1}{2}\)
c, x=? để A< 1
d, Tìm x\(\varepsilon\)Z để A\(\varepsilon\)Z
làm đc câu nào hay câu đây, càng nhiều càng tốt
cảm ơn nha
a. \(A=\left(\frac{2x^2+1}{x^2+1}\right):\left(\frac{1}{x-1}-\frac{2x}{\left(x^2+1\right)\left(x-1\right)}\right)\)
\(\Rightarrow A=\frac{2x^2+1}{x^2+1}:\left(\frac{x^2+1-2x}{\left(x-1\right)\left(x^2+1\right)}\right)\)
\(\Rightarrow A=\frac{2x^2+1}{x^2+1}:\left(\frac{\left(x-1\right)^2}{\left(x-1\right)\left(x^2+1\right)}\right)\)
\(\Rightarrow A=\frac{2x^2+1}{x^2+1}:\frac{x-1}{x^2+1}\)
\(\Rightarrow A=\frac{2x^2+1}{x^2+1}\cdot\frac{x^2+1}{x-1}\)\(\Rightarrow A=\frac{2x^2+1}{x-1}=\left(2x+2\right)+\frac{3}{x-1}\)
Cho biểu thức sau: Q=\(\frac{-7\sqrt{x}+7}{5\sqrt{x}-1}+\frac{2\sqrt{x}-2}{\sqrt{x}+2}+\frac{39\sqrt{x}+12}{5x+9\sqrt{x}-2}\)
1/Tìm điều kiện để Q có nghĩa và rút gọn Q
2/Tìm x để Q<=-3
3/Tìm x\(\varepsilon Z\)để Q\(\varepsilon Z\)
Cho biểu thức
\(B=\frac{2x-9}{x^2-5x+6}-\frac{x+3}{x-2}-\frac{2x+4}{3-x}\)
a)Rút gọn B
b)Tìm x thuộc Z để B thuộc Z
a) Điều kiện : \(x\ne2;x\ne3\)
\(B=\frac{2x-9}{x^2-5x+6}-\frac{x+3}{x-2}-\frac{2x+4}{3-x}=\frac{2x-9}{\left(x-2\right)\left(x-3\right)}-\frac{x+3}{x-2}+\frac{2x+4}{x-3}\)
\(=\frac{2x-9-\left(x-3\right)\left(x+3\right)+2\left(x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x-3\right)}=\frac{2x-9-x^2+9+2x^2-8}{\left(x-2\right)\left(x-3\right)}=\frac{x^2+2x-8}{\left(x-2\right)\left(x-3\right)}\)
\(=\frac{\left(x-2\right)\left(x+4\right)}{\left(x-2\right)\left(x-3\right)}=\frac{x+4}{x-3}\)
b) Điều kiện \(x\in Z;x\ne2;x\ne3\)
Có \(B=\frac{x+4}{x-3}\in Z\), mà x+4 và x-3 nguyên do x nguyên, nên
\(x+4⋮x-3\Leftrightarrow7⋮x-3\), do đó \(x-3\inƯ\left(7\right)=\left\{1;7;-1;-7\right\}\Rightarrow x\in\left\{4;10;2;-4\right\}\)
mà do x khác 2 (điều kiện) nên ta kết luận \(x\in\left\{4;10;-4\right\}\)
Cho A = \(\left(\frac{2x-3}{4x^2-12x+5}+\frac{3x-8}{13x-2x^2-20}-\frac{3}{2x-1}\right):\frac{21+2x-2x^2}{4x^2+4x-3}+1\)
a, Rút gọn .
b, Tìm \(x\in Z\)để \(A\in Z\).
c, Tìm x để \(A\ge0\)
a. ĐKXĐ : \(x\ne\frac{1}{2};\frac{5}{2};4;-\frac{3}{2};\frac{1\pm\sqrt{43}}{2}\)
\(A=\left(\frac{2x-3}{4x^2-12x+5}+\frac{3x-8}{13x-2x^2-20}-\frac{3}{2x-1}\right):\frac{21+2x-2x^2}{4x^2+4x-3}+\)
\(=\left(\frac{2x-3}{\left(2x-1\right)\left(2x-5\right)}-\frac{3x-8}{\left(2x-5\right)\left(x-4\right)}-\frac{3}{2x-1}\right).\frac{\left(2x-1\right)\left(2x+3\right)}{21+2x-2x^2}+1\)
\(=\frac{\left(2x-3\right)\left(x-4\right)-\left(3x-8\right)\left(2x-1\right)-3\left(2x-5\right)\left(x-4\right)}{\left(2x-1\right)\left(2x-5\right)\left(x-4\right)}.\frac{\left(2x-1\right)\left(2x+3\right)}{21+2x-2x^2}+1\)
\(=\frac{-10x^2+47x-56}{\left(2x-5\right)\left(x-4\right)}.\frac{2x+3}{-2x^2+2x+21}+1\) số to wa