Giai pt
a/\(\dfrac{x+2}{x-2}-\dfrac{2}{x^2-2x}=\dfrac{1}{x}\)
b/\(\dfrac{1}{x-1}-\dfrac{3x^2}{x^3-1}=\dfrac{2x}{x^2+x+1}\)
1.giải pt
a)\(\dfrac{16-x}{4}=\dfrac{2x+1}{3}\)
b)(2x+3)(1-3x)=9x\(^2\)-1
c)\(\dfrac{2x}{x+1}+\dfrac{x-1}{x}=\dfrac{2x^2+3x-1}{x^2+x}\)
a>16-x/4=2x+1/3
<=>3[16-x)=4(2x+1)
<=>48-3x=8x+8
<=>-3x-8x=8-48
<=>-5x=-40
<=>x=8
giải pt
a.\(\dfrac{x+5}{3\left(x-1\right)}+1=\dfrac{3x+7}{5\left(x-1\right)}\)
b.\(\dfrac{3x-1}{x-1}-\dfrac{2x+5}{x+3}-\dfrac{8}{x^2+2x-3}=1\)
a) \(\dfrac{x+5}{3\left(x-1\right)}+1=\dfrac{3x+7}{5\left(x-1\right)}\) ( đk: \(x\ne1\))
\(\Leftrightarrow\dfrac{5\left(x+5\right)}{15\left(x-1\right)}+\dfrac{15\left(x-1\right)}{15\left(x-1\right)}=\dfrac{3\left(3x+7\right)}{15\left(x-1\right)}\)
\(\Rightarrow5\left(x+5\right)+15\left(x-1\right)=3\left(3x+7\right)\)
\(\Leftrightarrow5x+25+15x-15=9x+21\)
\(\Leftrightarrow5x+15x-9x=21-25+15\)
\(\Leftrightarrow11x=11\Leftrightarrow x=1\) (loại)
Vậy tập nghiệm: \(S=\varnothing\)
b) \(\dfrac{3x-1}{x-1}-\dfrac{2x+5}{x+3}-\dfrac{8}{x^2+2x-3}=1\) (đk: \(x\ne1,x\ne-3\))
\(\Leftrightarrow\dfrac{\left(3x-1\right)\left(x+3\right)}{x^2+2x-3}-\dfrac{\left(2x+5\right)\left(x-1\right)}{x^2+2x-3}-\dfrac{8}{x^2+2x-3}=\dfrac{x^2+2x-3}{x^2+2x-3}\)
\(\Rightarrow\left(3x-1\right)\left(x+3\right)-\left(2x+5\right)\left(x-1\right)-8=x^2+2x-3\)
\(\Leftrightarrow3x^2+9x-x-3-2x^2+2x-5x+5-8=x^2+2x-3\)
\(\Leftrightarrow3x=3\Leftrightarrow x=1\) (loại)
Vậy tập nghiệm: \(S=\varnothing\)
Giai các ptr sau
a,\(\dfrac{1}{x-1}-\dfrac{3x^2}{x^3-1}=\dfrac{2x}{x^2+x+1}\)
b,\(\dfrac{8800}{x-2}-\dfrac{8800}{x}=20\)
c,\(\dfrac{1}{x}+\dfrac{1}{x+5}=\dfrac{1}{6}\)
d,\(\dfrac{x-1}{x}-\dfrac{1}{x+1}=\dfrac{2x-1}{x^2+x}\)
a: \(\Leftrightarrow x^2+x+1-3x^2=2x\left(x-1\right)\)
=>-2x^2+x+1-2x^2+2x=0
=>-4x^2+3x+1=0
=>4x^2-3x-1=0
=>4x^2-4x+x-1=0
=>(x-1)(4x+1)=0
=>x=1(loại) hoặc x=-1/4(nhận)
b: \(\Leftrightarrow\dfrac{440}{x-2}-\dfrac{440}{x}=1\)
=>x(x-2)=440x-440x+880
=>x^2-2x-880=0
=>\(x=1\pm\sqrt{881}\)
c: \(\Leftrightarrow\dfrac{x+5+x}{x\left(x+5\right)}=\dfrac{1}{6}\)
=>x^2+5x=6(2x+5)
=>x^2+5x-12x-30=0
=>x^2-7x-30=0
=>(x-10)(x+3)=0
=>x=10 hoặc x=-3
d: =>(x-1)(x+1)-x=2x-1
=>x^2-1-x=2x-1
=>x^2-x-2x=0
=>x(x-3)=0
=>x=0(loại) hoặc x=3(nhận)
giải bất pt
a.\(\dfrac{1-2x}{4}-2< \dfrac{1-6x}{8}\)
b.\(\dfrac{x-1}{3}-2x>\dfrac{3x+1}{2}\)
giải bất pt
a)\(\dfrac{1-2x}{4}-1< \dfrac{1-6x}{8}\)
b)\(\dfrac{x-1}{3}-2x>\dfrac{3x+1}{2}\)
A 1-2x/4-1<1-6x/8
<=>2(1-2x)-8<1-6x
<=>2-4x-8<1-6x
<=>-4x+6x<1-2+8
<=>2x<7
<=>x<7/2
a)\(\dfrac{1-2x}{4}-1< \dfrac{1-6x}{8}\)
\(\Leftrightarrow\dfrac{1-2x-4}{4}< \dfrac{1-6x}{8}\)
\(\Leftrightarrow8\left(-3-2x\right)< 4\left(1-6x\right)\)
\(\Leftrightarrow-24+16x< 4-24x\)
\(\Leftrightarrow40x< 28\)
\(\Leftrightarrow x< \dfrac{7}{10}\)
b)\(\dfrac{x-1}{3}-2x>\dfrac{3x+1}{2}\)
\(\Leftrightarrow\dfrac{x-1-6x}{3}>\dfrac{3x+1}{2}\)
\(\Leftrightarrow2\left(-5x-1\right)>3\left(3x+1\right)\)
\(\Leftrightarrow-10x-2>9x+3\)
\(\Leftrightarrow-19x>5\)
\(\Leftrightarrow x< \dfrac{-5}{19}\)
giải bất pt
a)\(\dfrac{1-2x}{4}-1< \dfrac{1-6x}{8}\)
b)\(\dfrac{x-1}{3}-2x>\dfrac{3x+1}{2}\)
Giai các bpt sau
a,\(\dfrac{5x^2-3}{5}+\dfrac{3x-1}{4}< \dfrac{x\left(2x+3\right)}{2}-5\)
b,\(\dfrac{5x-2}{-3}\)\(-\dfrac{2x^2-x}{-2}>\dfrac{x\left(1-3x\right)}{-3}-\dfrac{5x}{-4}\)
a: \(\Leftrightarrow4\left(5x^2-3\right)+5\left(3x-1\right)< 10x\left(2x+3\right)-100\)
\(\Leftrightarrow20x^2-12x+15x-5< 20x^2+30x-100\)
=>3x-5<=30x-100
=>30x-100>3x-5
=>27x>95
hay x>95/27
b: \(\Leftrightarrow4\left(5x-2\right)-6\left(2x^2-x\right)< 4x\left(1-3x\right)-15x\)
\(\Leftrightarrow20x-8-12x^2+6x< 4x-12x^2-15x\)
=>26x-8<-11x
=>37x<8
hay x<8/37
Giải các pt sau:
1)\(\dfrac{2x+1}{x^2-4}+\dfrac{2}{x+1}=\dfrac{3}{2-x}\)
2)\(\dfrac{3x+1}{1-3x}+\dfrac{3+x}{3-x}=2\)
3)\(\dfrac{8x-2}{3}=1+\dfrac{5-2x}{4}\)
4)
\(\dfrac{x}{x+1}-\dfrac{2x+3}{x}=\dfrac{-3}{x+1}-\dfrac{3}{x}\)
5)\(\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{4}{x^2-1}\)
6)\(\dfrac{2x+5}{2x}-\dfrac{x}{x+5}=0\)
giúp mình với cám ơn
1: Sửa đề: 2/x+2
\(\dfrac{2x+1}{x^2-4}+\dfrac{2}{x+2}=\dfrac{3}{2-x}\)
=>\(\dfrac{2x+1+2x-4}{x^2-4}=\dfrac{-3\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)
=>4x-3=-3x-6
=>7x=-3
=>x=-3/7(nhận)
2: \(\Leftrightarrow\dfrac{\left(3x+1\right)\left(3-x\right)+\left(3+x\right)\left(1-3x\right)}{\left(1-3x\right)\left(3-x\right)}=2\)
=>9x-3x^2+3-x+3-9x+x-3x^2=2(3x-1)(x-3)
=>-6x^2+6=2(3x^2-10x+3)
=>-6x^2+6=6x^2-20x+6
=>-12x^2+20x=0
=>-4x(3x-5)=0
=>x=5/3(nhận) hoặc x=0(nhận)
3: \(\Leftrightarrow x\cdot\dfrac{8}{3}-\dfrac{2}{3}=1+\dfrac{5}{4}-\dfrac{1}{2}x\)
=>x*19/6=35/12
=>x=35/38
Bài 1:tính
a)\(\dfrac{x^2-2^{ }}{x\left(x-1\right)^2}+\dfrac{2-x}{x\left(1-x\right)^2}\)
b)\(\dfrac{3}{2x}+\dfrac{3x-3}{2x-1}+\dfrac{2x^2+1}{4x^2-2x}\)
c)\(\dfrac{x}{x-1}+\dfrac{2}{x^2+x+1}+\dfrac{4x^2-1}{1-x^3}\)
\(a,=\dfrac{x^2-2+2-x}{x\left(x-1\right)^2}=\dfrac{x\left(x-1\right)}{x\left(x-1\right)^2}=\dfrac{1}{x-1}\\ b,=\dfrac{6x-3+6x^2-6x+2x^2+1}{2x\left(2x-1\right)}=\dfrac{8x^2-2}{2x\left(2x-1\right)}\\ =\dfrac{2\left(2x-1\right)\left(2x+1\right)}{2x\left(2x-1\right)}=\dfrac{2x+1}{x}\\ c,=\dfrac{x^3+x^2+x+2x-2+4x^2-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x^3+5x^2+3x-3}{x^3-1}\)