M=\(\dfrac{x+1}{2x-2}+\dfrac{3}{x^2-1}-\dfrac{x+3}{2x+2}\)
a) Rút gọn M
b) Tính x để M=5
Cho biểu thức: A = \(\dfrac{1}{x-1}+\dfrac{x}{x^2-1}\)và B = \(\dfrac{x^2-x}{2x+1}\) (x ≠ -\(\dfrac{1}{2}\),x ≠ 1)
a) Tính giá trị của B tại x = 3
b) Rút gọn M = A.B
c) Tìm x để M = \(\dfrac{1}{3}\)
`a,` Với `x=3`
\(B=\dfrac{x^2-x}{2x+1}\\ \Rightarrow\dfrac{3^2-3}{2\cdot3+1}\\ =\dfrac{9-3}{6+1}\\ =\dfrac{6}{7}\)
`b,` Ta có `M=A*B`
\(M=\left(\dfrac{1}{x-1}+\dfrac{x}{x^2-1}\right)\cdot\dfrac{x^2-x}{2x+1}\\ =\left(\dfrac{1}{x-1}+\dfrac{x}{\left(x-1\right)\left(x+1\right)}\right)\cdot\dfrac{x\left(x-1\right)}{2x+\text{ }1}\\ =\left(\dfrac{x+1}{\left(x-1\right)\left(x+1\right)}+\dfrac{x}{\left(x-1\right)\left(x+1\right)}\right)\cdot\dfrac{x\left(x-1\right)}{2x+1}\\ =\dfrac{x+1+x}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{x\left(x-1\right)}{2x+1}\\ =\dfrac{2x+1}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{x\left(x-1\right)}{2x+1}\\ =\dfrac{x}{x+1}\)
`c,` Để `M=1/2`
`=> x/(x+1)=1/3`
`<=> (3x)/(3(x+1))= (x+1)/(3(x+1))`
`<=> 3x=x+1`
`<=>3x-x=1`
`<=>2x=1`
`<=>x=1/2`
M=\(\left(\dfrac{x^2-2x}{2x^2+8}-\dfrac{2x^2}{8-4x+2x^2-x^3}\right)\left(1-\dfrac{1}{x}-\dfrac{2}{x^2}\right)\)
a) tìm ĐKXĐ của x
b) rút gọn M
c) tìm x để M≥-3
a: ĐKXĐ: x<>2; x<>0
b: \(M=\left(\dfrac{x^2-2x}{2\left(x^2+4\right)}+\dfrac{2x^2}{\left(x-2\right)\left(x^2+4\right)}\right)\cdot\dfrac{x^2-x-2}{x^2}\)
\(=\dfrac{\left(x^2-2x\right)\left(x-2\right)+4x^2}{2\left(x-2\right)\left(x^2+4\right)}\cdot\dfrac{\left(x-2\right)\left(x+1\right)}{x^2}\)
\(=\dfrac{x^3-2x^2-2x^2+4x}{2\left(x^2+4\right)}\cdot\dfrac{x+1}{x^2}\)
\(=\dfrac{x}{2}\cdot\dfrac{x+1}{x^2}=\dfrac{x+1}{2x}\)
c: M>=-3
=>(x+1+6x)/2x>=0
=>(7x+1)/x>=0
=>x>0 hoặc x<=-1/7
M= \(\left(\dfrac{x-1}{2x-2}-\dfrac{x+3}{2x+2}\right):\left(1-\dfrac{x-3}{x-1}\right)\)
Điều kiện: x khác -1, +1
a, Rút gọn M
b, Tính giá trị của M tại x=\(\dfrac{-1}{2}\)
a: \(M=\left(\dfrac{\left(x-1\right)\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}-\dfrac{\left(x+3\right)\left(x-1\right)}{2\left(x+1\right)\left(x-1\right)}\right):\dfrac{x-1-x+3}{x-1}\)
\(=\dfrac{x^2-1-x^2-2x+3}{2\left(x-1\right)\left(x+1\right)}\cdot\dfrac{x-1}{2}\)
\(=\dfrac{-2x+2}{2\left(x+1\right)}\cdot\dfrac{1}{2}=\dfrac{-x+1}{2}\)
b: Thay x=-1/2 vào M, ta được:
\(M=\dfrac{\dfrac{1}{2}+1}{2}=\dfrac{3}{2}:2=\dfrac{3}{4}\)
a, \(M=\left(\dfrac{x^2-1-\left(x+3\right)\left(x-1\right)}{2\left(x-1\right)\left(x+1\right)}\right):\left(\dfrac{x-1-x+3}{x-1}\right)\)
\(=\left(\dfrac{-1+x-3x-3}{2\left(x-1\right)\left(x+1\right)}\right):\dfrac{2}{x-1}=\dfrac{-2x-4}{2\left(x-1\right)\left(x+1\right)}:\dfrac{2}{x-1}=\dfrac{-\left(x+2\right)}{2\left(x+1\right)}\)
b, Thay x =-1/2 vào ta đc
\(-\dfrac{\left(\dfrac{-1}{2}+2\right)}{2\left(-\dfrac{1}{2}+1\right)}=\dfrac{-\dfrac{3}{2}}{2\left(\dfrac{1}{2}\right)}=\dfrac{-3}{2}\)
a, \(M=\left(\dfrac{x^2-1-\left(x+3\right)\left(x-1\right)}{2\left(x-1\right)\left(x+1\right)}\right):\left(\dfrac{x-1-x+3}{x-1}\right)\)
\(=\dfrac{-2x+2}{2\left(x-1\right)\left(x+1\right)}:\dfrac{2}{x-1}=\dfrac{-2\left(x-1\right)^2}{4\left(x-1\right)\left(x+1\right)}=\dfrac{-\left(x-1\right)}{2\left(x+1\right)}\)
b, Thay x = -1/2 vào ta đc
\(M=\dfrac{\dfrac{1}{2}+1}{2\left(\dfrac{-1}{2}+1\right)}=\dfrac{\dfrac{3}{2}}{\dfrac{2.1}{2}}=\dfrac{3}{2}\)
Cho biểu thức A=\(\left(\dfrac{2-3x}{x^2+2x-3}-\dfrac{x+3}{1-x}-\dfrac{x+1}{x+3}\right):\dfrac{3x+12}{x^3-1}\)
và B=\(\dfrac{x^2+x-2}{x^3-1}\)
a Rút gọn biểu thức M=A.B
b Tìm x thuộc Z để M thuộc Z
c Tìm GTLN của biểu thức N=\(A^{-1}-B\)
a. \(A=\left(\dfrac{2-3x}{x^2+2x-3}-\dfrac{x+3}{1-x}-\dfrac{x+1}{x+3}\right):\dfrac{3x+12}{x^3-1}\left(ĐKXĐ:x\ne1;x\ne-3\right)\)
\(=\left(\dfrac{2-3x}{\left(x-1\right)\left(x+3\right)}+\dfrac{x+3}{x-1}-\dfrac{x+1}{x+3}\right):\dfrac{3x+12}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\left(\dfrac{2-3x}{\left(x-1\right)\left(x+3\right)}+\dfrac{\left(x+3\right)^2}{\left(x-1\right)\left(x+3\right)}-\dfrac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+3\right)}\right):\dfrac{3x+12}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{2-3x+x^2+6x+9-x^2+1}{\left(x-1\right)\left(x+3\right)}:\dfrac{3x+12}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{3x+12}{\left(x-1\right)\left(x+3\right)}:\dfrac{3x+12}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{3x+12}{\left(x-1\right)\left(x+3\right)}.\dfrac{\left(x-1\right)\left(x^2+x+1\right)}{3x+12}=\dfrac{x^2+x+1}{x+3}\)
\(M=A.B=\dfrac{x^2+x+1}{x+3}.\dfrac{x^2+x-2}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x^2+x-2}{x+3}\)
b. -Để M thuộc Z thì:
\(\left(x^2+x-2\right)⋮\left(x+3\right)\)
\(\Rightarrow\left(x^2+3x-2x-6+4\right)⋮\left(x+3\right)\)
\(\Rightarrow\left[x\left(x+3\right)-2\left(x+3\right)+4\right]⋮\left(x+3\right)\)
\(\Rightarrow4⋮\left(x+3\right)\)
\(\Rightarrow x+3\in\left\{1;2;4;-1;-2;-4\right\}\)
\(\Rightarrow x\in\left\{-2;-1;1;-4;-5;-7\right\}\)
c. \(A^{-1}-B=\dfrac{x+3}{x^2+x+1}-\dfrac{x^2+x-2}{x^3-1}\)
\(=\dfrac{x+3}{x^2+x+1}-\dfrac{x^2+x-2}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{\left(x+3\right)\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}-\dfrac{x^2+x-2}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{x^2-x+3x-3-x^2-x+2}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{1}{x^2+x+1}\)
\(=\dfrac{1}{x^2+2.\dfrac{1}{2}x+\dfrac{1}{4}+\dfrac{3}{4}}=\dfrac{1}{\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}}\le\dfrac{1}{\dfrac{3}{4}}=\dfrac{4}{3}\)
\(Max=\dfrac{4}{3}\Leftrightarrow x=\dfrac{-1}{2}\)
cho M= \(\left(\dfrac{\sqrt{x}+1}{\sqrt{2x}+1}+\dfrac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}-1\right)\div\left(1+\dfrac{\sqrt{x}}{\sqrt{2x}+1}-\dfrac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}\right)\)
a) rút gọn M
b) tính giá trị của M khi \(x=\dfrac{1}{3}\left(3+2\sqrt{2}\right)\)
c) tìm tất cả các giá trị của x sao cho B=x-4
d) tìm khoảng giá trị của x sao cho B <\(-\dfrac{2}{3}\)
Lm nhanh giúp mk nhé mk đang cần gấp
a) Ta có: \(M=\left(\dfrac{\sqrt{x}+1}{\sqrt{2x}+1}+\dfrac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}-1\right):\left(1+\dfrac{\sqrt{x}}{\sqrt{2x}+1}-\dfrac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}\right)\)
\(=\left(\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{2x}-1\right)+\sqrt{x}\left(\sqrt{2x}+1\right)^2-2x+1}{\left(\sqrt{2x}+1\right)\left(\sqrt{2x}-1\right)}\right):\left(\dfrac{2x-1+\sqrt{x}\left(\sqrt{2x}-1\right)-\sqrt{x}\left(\sqrt{2x}+1\right)^2}{\left(\sqrt{2x}+1\right)\left(\sqrt{2x}-1\right)}\right)\)
\(=\dfrac{x\sqrt{2}-\sqrt{x}+\sqrt{2x}-1+\sqrt{x}\left(2x+2\sqrt{2x}+1\right)-2x+1}{2x-1+x\sqrt{2}-\sqrt{x}-\sqrt{x}\left(2x+2\sqrt{2x}+1\right)}\)
\(=\dfrac{x\sqrt{2}-\sqrt{x}+\sqrt{2x}-2x+2x\sqrt{x}+2\sqrt{2x}+\sqrt{x}}{2x-1+x\sqrt{2}-\sqrt{x}-2x\sqrt{x}-2\sqrt{2x}-\sqrt{x}}\)
\(=\dfrac{x\sqrt{2}+3\sqrt{2x}-2x+2x\sqrt{x}}{x\sqrt{2}-2\sqrt{2x}+2x-2\sqrt{x}-2x\sqrt{x}}\)
Cho biểu thức: M= \(\dfrac{x+1}{2x-2}+\dfrac{3}{x^2^{ }-1}-\dfrac{x+3}{2x+2}\)
a) Rút gọn M
b) Tìm x để M=5
a: \(M=\dfrac{x+1}{2\left(x-1\right)}+\dfrac{3}{\left(x-1\right)\left(x+1\right)}-\dfrac{x+3}{2\left(x+1\right)}\)
\(=\dfrac{x^2+2x+1+6-x^2-2x+3}{2\left(x-1\right)\left(x+1\right)}=\dfrac{5}{x^2-1}\)
b: Để M=5 thì x^2-1=1
=>x^2=2
=>\(x=\pm\sqrt{2}\)
Câu 1: Cho biểu thức P= \(\dfrac{x+1}{3x-x^2}:\left(\dfrac{3+x}{3-x}-\dfrac{3-x}{3+x}-\dfrac{12x^2}{x^2-9}\right)\)
a)Rút gọn P
b)Tính P khi |2x-1|=5
c)Tìm giá trị x để P<0
Câu 2:Cho biểu thức M=\(\left(\dfrac{x}{x+5}-\dfrac{5}{5-x}+\dfrac{10x}{x^2-25}\right).\left(1-\dfrac{5}{x}\right)\)
a)Rút gọn M
b)Tìm x thộc Z để M thuộc Z
c)Tìm x thuộc Z để M nguyên dương
Câu 3:Cho biểu thức B=\(\left(\dfrac{2x}{2x^2-5x+3}-\dfrac{5}{2x-3}\right):\left(3+\dfrac{2}{1-x}\right)\)
a)Rút gọn B
b)Tìm x để B=\(\dfrac{1}{x^2}\)
c)Tìm x để B>0
Câu 4:Cho biểu thức C=\(\left(\dfrac{1}{x^2+1}-\dfrac{x+1}{x^4-1}\right):\dfrac{x+1}{x^5+x^4-x-1}\)
a)Rút gọn C
b)Tìm x để C=0
c)Tìm giá trị nhỏ nhất của C
Làm nhanh giúp mình nhe sắp thi cuối kỳ rồi thanks <3
Câu 1 :
a) Rút gọn P :
\(P=\dfrac{x+1}{3x-x^2}:\left(\dfrac{3+x}{3-x}-\dfrac{3-x}{3+x}-\dfrac{12x^2}{x^2-9}\right)\)
\(P=\dfrac{x+1}{x\left(3-x\right)}:\left[\dfrac{\left(3+x\right)^2}{\left(3-x\right)\left(3+x\right)}-\dfrac{\left(3-x\right)^2}{\left(3-x\right)\left(3+x\right)}-\dfrac{12x^2}{\left(3-x\right)\left(3+x\right)}\right]\)
\(P=\dfrac{x+1}{x\left(3-x\right)}:\left(\dfrac{9+6x+x^2-9+6x-x^2-12x^2}{\left(3-x\right)\left(3+x\right)}\right)\)
\(P=\dfrac{x+1}{x\left(3-x\right)}:\dfrac{12x-12x^2}{\left(3-x\right)\left(x+3\right)}\)
\(P=\dfrac{x+1}{x\left(3-x\right)}.\dfrac{\left(3-x\right)\left(x+3\right)}{12x\left(1-x\right)}\)
\(P=\dfrac{\left(x+1\right)\left(x+3\right)}{12x^2\left(1-x\right)}\)
Cho biểu thức: \(M=\dfrac{x+1}{2x-2}-\dfrac{x^2+3}{2x^2-2}\)
a) Rút gọn M
b) Tính GTNN,GTLN của M khi x\(\in\) {0; 0,5}
Cíu mik với ...
a: \(M=\dfrac{x^2+2x+1-x^2-3}{2\left(x-1\right)\left(x+1\right)}=\dfrac{2\left(x-1\right)}{2\left(x-1\right)\left(x+1\right)}=\dfrac{1}{x+1}\)
b: x thuộc {0;0,5}
=>x=0 hoặc x=0,5
Khi x=0 thì M=1/0+1=1
Khi x=0,5 thì M=1/0,5+1=1/1,5=2/3
=>M min=2/3 và M max=1
C = \(\dfrac{5x+1}{x^3-1}\)- \(\dfrac{1-2x}{x^2+x+1}\)- \(\dfrac{2}{1-x}\)
a. rút gọn C
b. tính giá trị của C khi /x/= 4
c. tìm x để C>0
d. tìm x thuộc Z để M thuộc Z
giúp mik ạ T_T
a: \(C=\dfrac{5x+1+\left(2x-1\right)\left(x-1\right)+2x^2+2x+2}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{2x^2+7x+3+2x^2-2x-x+1}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{4}{x-1}\)
b: x=4 thì C=4/(4-1)=4/3
Khi x=-4 thì C=4/(-4-1)=-4/5
c: C>0
=>x-1>0
=>x>1