Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
1. A = -4 phần x+2
2. 2x^2 + x = 0 => x = 0 hoặc x = -1/2
Với x = 0 thì A = -2
Với x = -1/2 thì A = -8/3
3. A = 1/2 => -4 phần x + 2 = 1/2
<=> -8 = x + 2
<=> x = -10
4. A nguyên dương => A > 0
=> -4 phần x + 2 > 0
Do -4 < 0 nên -4 phần x + 2 > 0 khi x + 2 < 0
=> x < -2
A=(1/x-2 - (2x/(2-x)(2+x) - 1/2+x) ) *(2-x)/x
=(1/x-2 - x^2+5x-2/(2-x)(2+x))*2-x/x
=(-x^3-4x^2+12x/(x-2)(2-x)(2+x))*2-x/x
= - x(x-2)(x+6)(2-x)/x(x-2)(2-x)(2+x)
= - x+6/x+2
\(A=\frac{1}{x+2}+\frac{1}{x-2}+\frac{x^2+1}{x^2-4}\)
\(=\frac{x-2}{\left(x-2\right)\left(x+2\right)}+\frac{x+2}{\left(x-2\right)\left(x+2\right)}+\frac{x^2+1}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{x^2+2x+1}{\left(x-2\right)\left(x+2\right)}=\frac{\left(x+1\right)^2}{\left(x-2\right)\left(x+2\right)}\)
Với \(\forall x\in\left[-2;2\right]\) thì \(\left(x-2\right)\left(x+2\right)< 0\Rightarrow\frac{\left(x+1\right)^2}{\left(x-2\right)\left(x+2\right)}< 0\Rightarrow A< 0\)
a) MTC : \(\left(x+1\right)\left(x^2-x+1\right)\)
Quy đồng :
\(\frac{x-1}{x^3+1}=\frac{x-1}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(\frac{2x}{x^2-x+1}=\frac{2x\left(x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(\frac{2}{x+1}=\frac{2\left(x^2-x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
b ) MTC : \(10x\left(2y-x\right)\left(2y+x\right)\)
\(\frac{7}{5x}=\frac{7.2.\left(2y-x\right)\left(2y+x\right)}{10x\left(2y-x\right)\left(2y+x\right)}\)
\(\frac{4}{x-2y}=\frac{-4.10x.\left(2y+x\right)}{10x\left(2y-x\right)\left(2y+x\right)}=\frac{-40x\left(2y+x\right)}{10x\left(2y-x\right)\left(2y+x\right)}\)
\(\frac{x-y}{8y^2-2x^2}=\frac{x-y}{2\left(4y^2-x^2\right)}=\frac{x-y}{2\left(2y-x\right)\left(2y+x\right)}=\frac{5x\left(x-y\right)}{10x\left(2y-x\right)\left(2y+x\right)}\)
c ) MTC : \(\left(x+2\right)^3\)
\(\frac{6x^2}{x^3+6x^2+12x+8}=\frac{6x^2}{\left(x+2\right)^3}\)
\(\frac{3x}{x^2+4x+4}=\frac{3x}{\left(x+2\right)^2}=\frac{3x\left(x+2\right)}{\left(x+2\right)^3}\)
\(\frac{2}{2x+4}=\frac{1}{x+2}=\frac{\left(x+2\right)^2}{\left(x+2\right)^3}\)
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 = \(\left\{\frac{11}{27}\right\}\)
<=>
\(\left(x-1\right)\left(x+2\right)\left(x+3\right)\left(x+6\right)=\left(x^2+5x-6\right)\left(x^2+5x+6\right)\)
Đặt \(x^2+5x=a\)
=> \(\left(a-6\right)\left(a+6\right)=a^2-36\ge-36\)
\(x\left(x+5\right)=0\) thì biểu thức nhỏ nhất
<=> x = 0 hoặc x = -5
1. \(A=\frac{\left(2x^2-2\right)\left(x+1\right)}{x^2+2x+1}=\frac{2\left(x+1\right)\left(x-1\right)\left(x+1\right)}{\left(x+1\right)^2}=2\left(x-1\right)\)
2)
a) cùng tử \(\frac{x^3-1}{x^2+1}=\frac{\left(x-1\right)\left(x^2+x+1\right)}{x^2+1}\)
\(\frac{x-1}{x+1}=\frac{\left(x-1\right)\left(x^2+x+1\right)}{\left(x+1\right)\left(x^2+x+1\right)}\)
b) cùng mẫu
\(\frac{1}{x^2-1}=\frac{x^3-8}{\left(x^2-1\right)\left(x^3-8\right)}\)
\(\frac{1}{x^3-8}=\frac{x^2-1}{\left(x^2-1\right)\left(x^3-8\right)}\)
3) cM
\(\frac{x^2-9}{x-3}=\frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)}=x+3\)
\(\frac{x^2+5x+6}{x+2}=\frac{x^2+2x+3x+6}{x+2}=\frac{x\left(x+2\right)+3\left(x+2\right)}{x+2}=\frac{\left(x+2\right)\left(x+3\right)}{x+2}=x+3\)
Vậy .......