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\(A=\frac{\left|x-1\right|+\left|x\right|-x}{3x^2+4x+1}=\frac{1-x-x-x}{3x^2+3x+x+1}=\frac{1-3x}{\left(x+1\right)\left(3x+1\right)}\)
\(B=\frac{\left|2x-1\right|+x}{3x^2-22x+7}=\frac{1-2x+x}{3x^2-21x-x+7}=\frac{1-x}{\left(x-7\right)\left(3x-1\right)}\)
Bài 2:
a: \(B=\left(\dfrac{x}{\left(x-2\right)\left(x+2\right)}-\dfrac{6}{3\left(x-2\right)}+\dfrac{1}{x-2}\right):\left(\dfrac{x^2-4+16-x^2}{x+2}\right)\)
\(=\left(\dfrac{x}{\left(x-2\right)\left(x+2\right)}-\dfrac{2}{x-2}+\dfrac{1}{x-2}\right):\dfrac{12}{x+2}\)
\(=\left(\dfrac{x}{\left(x-2\right)\left(x+2\right)}-\dfrac{1}{x-2}\right):\dfrac{12}{x+2}\)
\(=\dfrac{x-x-2}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x+2}{12}=\dfrac{-1}{6\left(x-2\right)}\)
b: Thay x=1/2 vào B, ta được:
\(B=\dfrac{-1}{6\cdot\left(\dfrac{1}{2}-2\right)}=\dfrac{-1}{6\cdot\dfrac{-3}{2}}=\dfrac{1}{9}\)
Thay x=-1/2 vào B, ta được:
\(B=\dfrac{-1}{6\cdot\left(-\dfrac{1}{2}-2\right)}=-\dfrac{1}{15}\)
c: Để B=2 thì \(\dfrac{-1}{6\left(x-2\right)}=2\)
=>6(x-2)=-1/2
=>x-2=-1/12
hay x=23/12
a) \(x^2-5x+6< 0\)
\(\Leftrightarrow x^2-2x-3x+6< 0\)
\(\Leftrightarrow x\left(x-2\right)-3\left(x-2\right)< 0\)
\(\Leftrightarrow\left(x-2\right)\left(x-3\right)< 0\)
\(\Leftrightarrow\hept{\begin{cases}x-2>0\\x-3< 0\end{cases}\Leftrightarrow\hept{\begin{cases}x>2\\x< 3\end{cases}}}\)
\(\Leftrightarrow2< x< 3\)
Vậy \(2< x< 3\)là các giá trị cần tìm của bất phương trình
b) \(\frac{2x\left(3x-5\right)}{x^2+1}< 0\)
\(\Leftrightarrow2x\left(3x-5\right)< 0\)(vì \(x^2+1>0\forall x\) )
\(\Leftrightarrow\hept{\begin{cases}2x>0\\3x-5< 0\end{cases}\Leftrightarrow\hept{\begin{cases}x>0\\3x< 5\end{cases}\Leftrightarrow}\hept{\begin{cases}x>0\\x< \frac{5}{3}\end{cases}}}\)
\(\Leftrightarrow0< x< \frac{5}{3}\)
Vậy \(0< x< \frac{5}{3}\)là các giá trị cần tìm của bất phương trình
\(\left(4x-1\right)^3-\left(4x-3\right)\left(16x^2+3\right)\)
\(=\left(4x\right)^3-3.\left(4x\right)^2.1+3.4x.1^2-1^3-\left(4x-3\right)\left(16x^2+3\right)\)
\(=64x^3-48x^2+12x-1-64x^3-12x-48x^2-9\)
\(=9\)
Vì kết quả là hằng số nên biểu thức trên không phụ thuộc vào x
b, \(=\frac{x^2+2.5.x+25+x^2-2.x.5+25}{x^2+25}\)
\(=\frac{2x^2+50}{x^2+25}=\frac{2\left(x^2+50\right)}{x^2+50}=2\)
1.
<=> 7 - 2x - 4 = -x - 4
<=> -2x + x = -4 -7 + 4
<=> -x = -7
<=> x = 7
Vậy S = { 7 }
2.
<=> \(\frac{2\left(3x-1\right)}{6}\)= \(\frac{3\left(2-x\right)}{6}\)
<=> 2( 3x - 1 ) = 3( 2 - x )
<=> 6x -2 = 6 - 3x
<=> 6x + 3x = 6 + 2
<=> 9x = 8
<=> x = \(\frac{8}{9}\)
Vậy S = \(\left\{\frac{8}{9}\right\}\)
3.
<=> \(\frac{6x+10}{3}-\frac{x}{2}=5-\frac{3x+3}{4}\)
<=> \(\frac{4\left(6x+10\right)}{12}-\frac{6x}{12}=\frac{60}{12}-\frac{3\left(3x+3\right)}{12}\)
<=> 4( 6x + 10 ) - 6x = 60 - 3( 3x + 3 )
<=> 24x + 40 - 6x = 60 - 9x -9
<=> 18x + 40 = 51 - 9x
<=> 18x + 9x = 51 - 40
<=> 27x = 11
<=> x = \(\frac{11}{27}\)
Vậy S = \(\left\{\frac{11}{27}\right\}\)
<=>
\(\frac{1}{\left(x+1\right)\left(x+2\right)}-\frac{2}{\left(x+2\right)^2}+\frac{1}{\left(x+2\right)\left(x+3\right)}\)
\(=\frac{\left(x+2\right)\left(x+3\right)-2\left(x+1\right)\left(x+3\right)+\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
\(=\frac{\left(x+3\right)\left(x+2-2x-2\right)+x^2+2x+x+2}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
\(=\frac{\left(x+3\right)\left(-x\right)+x^2+3x+2}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
\(=\frac{-x^2-3x+x^2+3x+2}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}=\frac{2}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
ĐKXD: x\(\ne\)-1,-2,-3
Ta có
\(\frac{1}{\left(x+1\right)\left(x+2\right)}\)-\(\frac{2}{\left(x+2\right)^2}\)+\(\frac{1}{\left(x+2\right)\left(x+3\right)}\)
=\(\frac{\left(x+2\right)\left(x+3\right)-2\left(x+1\right)\left(x+3\right)+\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
=\(\frac{\left(x+2\right)\left(x+3+x+1\right)-2\left(x^2+4x+3\right)}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
=\(\frac{\left(x+2\right)\left(2x+4\right)-2x^2-8x-6}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
=\(\frac{2x^2+8x+8-2x^2-8x-6}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
=\(\frac{2}{\left(x+1\right)\left(x+2\right)^2\left(x+3\right)}\)
Chúc bạn học tốt
a)1-6x2-x =0<=>-(6x2+x-1)=0<=>6x2+x-1=0
<=>(6x2+3x)-(2x+1)=0<=>3x(2x+1)-(2x+1)=0
<=>(3x-1)(2x+1)=0
=>3x-1=0 hoặc 2x+1=0=>x=\(\dfrac13\) hoặc x=-\(\dfrac12\)
Vậy S={\(\dfrac13\);-\(\dfrac12\)}
b)12x2+13x+3=0<=>12x2+9x+4x+3=0<=>(12x2+9x)+(4x+3)=0
<=>3x(4x+3)+(4x+3)=0<=>(3x+1)(4x+3)=0
=>3x+1=0 hoặc 4x+3=0 <=>x=-\(\dfrac13 \) hoặc x=-\(\dfrac34\)
Vậy S={-\(\dfrac13 \);-\(\dfrac34 \)}
c)x3-11x2+30x=0<=>x(x2-11x+30)=0<=>x[(x2-6x)-(5x-30)]=0
<=>x[x(x-6)-5(x-6)]=0<=>x(x-5)(x-6)=0
=>x=0 hoặc x-5=0 hoặc x-6=0=>x=0 hoặc x=5 hoặc x=6
Vậy S={0;5;6}
d)Ta có:(x2+x+1)(x2+x+2)-12=0
Đặt:t=x2+x+1
Khi đó:a(a+1)-12=0<=>a2+a-12=0<=>(a2+4a)-(3a+12)=0
<=>a(a+4)-3(a+4)=0<=>(a-3)(a+4)=0
hay (x2+x-2)(x2+x+5)=0
<=>(x-1)(x+2)(x2+x+5)=0(x2+x-2=(x-1)(x+2))
=>x-1=0 hoặc x+2=0(vì x2+x+5=(x+\(\dfrac12\))2+\(\dfrac{19}{4}\)>0)
=>x=1 hoặc x=-2
Vậy S={1;-2}
e)Ta có:2x2+x+6>x2+x+6=(x+\(\dfrac12\))2+\(\dfrac{23}{4}\)>0
nên PT vô nghiệm
Vậy S=\(\varnothing\)