(2x + 1)(3x + 3) = 0

<=> 2x + 1 = 0 hoặc 3x + 3 = 0

<=> x = -1/2 hoặc x = -1

\(\left(2x+1\right)\left(3x+3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}2x+1=0\\3x+3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=-1\\3x=-3\end{cases}\Leftrightarrow}}\orbr{\begin{cases}x=\frac{-1}{2}\\x=-1\end{cases}}\)

Vậy ...

\(\frac{x^3+x^2-x-1}{x^3+2x-5}\)

\(\Leftrightarrow\frac{x^3+x^2-x-1}{x^3+2x-5}=0\)

\(\Leftrightarrow\frac{x^2\left(x+1\right)-\left(x+1\right)}{x^3+2x-5}=0\)

\(\Leftrightarrow\frac{\left(x+1\right)\left(x^2-1^2\right)}{x^3+2x-5}=0\)

\(\Leftrightarrow\frac{\left(x+1\right)\left(x+1\right)\left(x+1\right)}{x^3+2x-5}=0\)

\(\Leftrightarrow\frac{\left(x+1\right)^2\left(x-1\right)}{x^3+2x-5}=0\)

\(\Leftrightarrow\left(x+1\right)^2\left(x-1\right)=0\)

\(\Leftrightarrow x=\pm1\)

Vậy \(x\in\left\{\pm1\right\}\)

\(\frac{x^3+x^2-x-1}{x^3+2x-5}=\frac{x^2\left(x+1\right)-\left(x+1\right)}{x^3+2x-5}\)

\(=\frac{\left(x+1\right)\left(x^2-1\right)}{x^3+2x-5}\)

Để \(\frac{x^3+x^2-x-1}{x^3+2x-5}=0\Leftrightarrow\left(x-1\right)\left(x^2-1\right)=0\left(x^3+2x-5\ne0\right)\)

\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\x^2-1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=1\\x^2=1\end{cases}\Leftrightarrow x=\pm}\)

Vậy x={-1;1}

1) \(\frac{7}{8}x-5\left(x-9\right)=\frac{20x+1,5}{6}\)

<=> \(\frac{21x}{24}-\frac{100\left(x-9\right)}{24}=\frac{80x+6}{24}\)

<=> 21x - 100x + 900 = 80x + 6

<=> -79x - 80x = 6 - 900

<=> -159x = -894

<=> x = 258/53

Vậy S = {258/53}

2) \(\frac{\left(2x+1\right)^2}{5}-\frac{\left(x+1\right)^2}{3}=\frac{7x^2-14x-5}{15}\)

<=> \(\frac{3\left(4x^2+4x+1\right)}{15}-\frac{5\left(x^2+2x+1\right)}{15}=\frac{7x^2-14x-5}{15}\)

<=> 12x² + 12x + 3 - 5x² - 10x - 5 = 7x² - 14x - 5

<=> 7x² + 2x - 7x² + 14x = -5 + 2

<=> 16x = 3

<=> x = 3/16

Vậy S  = {3/16}

3) 4(3x - 2) - 3(x - 4) = 7x+  10

<=> 12x - 8 - 3x + 12 = 7x + 10

<=> 9x - 7x = 10 - 4

<=> 2x = 6

<=> x = 3

Vậy S = {3}

4) \(\frac{\left(x+10\right)\left(x+4\right)}{12}-\frac{\left(x+4\right)\left(2-x\right)}{4}=\frac{\left(x+10\right)\left(x-2\right)}{3}\)

<=> \(\frac{x^2+14x+40}{12}+\frac{3\left(x^2+2x-8\right)}{12}=\frac{4\left(x^2+8x-20\right)}{12}\)

<=> x² + 14x + 40 + 3x² + 6x - 24 = 4x² + 32x - 80

<=> 4x² + 20x - 4x² - 32x = -80 - 16

<=> -12x = -96

<=> x = 8

Vậy S = {8}

tớ đang cần gấp 

Đề như sai rồi bạn ơi. 

Câu 2: 6x² + 7x - 3

= 6x² + 9x - 2x - 3

= 3x(2x +3) - (2x + 3)

= (3x - 1)(2x + 3)

Ta có: \(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}=1\)

\(\Rightarrow\left(a+b+c\right)\left(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\right)=a+b+c\)

\(\Rightarrow\left(\frac{a^2}{b+c}+\frac{b^2}{c+a}+\frac{c^2}{a+b}\right)+\left(a+b+c\right)=a+b+c\)

\(\Rightarrow\left(\frac{a^2}{b+c}+\frac{b^2}{c+a}+\frac{c^2}{a+b}\right)=0\)(đpcm)

thanks

a) 0,75x(x + 5) = (x + 5)(3 - 1,25x)

<=> 0,75x(x + 5) - (x + 5)(3 - 1,25x) = (x + 5)(3 - 1,25x) - (x + 5)(3 - 1,25x)

<=> 0,75x(x + 5) - (x + 5)(3 - 1,25x) = 0

<=> (x + 5)(0,75 + 1,25x - 3) = 0

<=> (x + 5)(2x - 3) = 0

<=> x + 5 = 0 hoặc 2x - 3 = 0

<=> x = -5 hoặc x = 3/2

b) 4/5 - 3 = 1/5x(4x - 15)

<=> -11/5 = x(4x - 15)/5

<=> -11 = x(4x - 15)

<=> -11 = 4x² - 15x

<=> 11 + 4x² - 15x = 0 

<=> 4x² - 4x - 11x + 11 = 0

<=> 4x(x - 1) - 11(x - 1) = 0

<=> (4x - 11)(x - 1) = 0

<=> 4x - 11 = 0 hoặc x - 1 = 0

<=> x = 11/4 hoặc x = 1

c) \(\left(x-3\right)-\frac{\left(x-3\right)\left(2x-5\right)}{6}=\frac{\left(x-3\right)\left(3-x\right)}{4}\)

<=> 12x - 36 - 2(x - 3)(2x - 5) = 3(x - 3)(3 - x)

<=> 12x - 36 - 4x² + 10x + 12x - 30 = 9x - 3x² - 27 + 9x

<=> 34x - 66 - 4x² = 18x - 3x² - 27

<=> 34x - 66 - 4x² - 18x + 3x² + 27 = 0

<=> 16x - 39x - x² = 0

<=> x² - 16x + 39x = 0

<=> (x - 3)(x - 13) = 0

<=> x - 3 = 0 hoặc x - 13 = 0

<=> x = 3 hoặc x = 13

d) \(\frac{\left(3x+1\right)\left(3x-2\right)}{3}+5\left(3x+1\right)=\frac{2\left(2x+1\right)\left(3x+1\right)}{3}+2x\left(3x+1\right)\)

<=> (3x + 1)(3x - 2) + 15(3x + 1) = 2(2x + 1)(3x + 1) + 6x(3x + 1)

<=> 9x² - 6x + 3x - 2 + 45x + 15 = 12x³ + 4x + 6x + 2 + 18x² + 6x

<=> 9x² + 42x + 13 = 30x² + 16x + 2

<=> 9x² + 42x + 13 - 30x² - 16x - 2 = 0

<=> -21x² + 26x + 11 = 0

<=> 21x² - 26x - 11 = 0

<=> 21x² + 7x - 33x - 11 = 0

<=> 7x(3x + 1) - 11(3x + 1) = 0

<=> (7x - 11)(3x + 1) = 0

<=> 7x - 11 = 0 hoặc 3x + 1 = 0

<=> x = 11/7 hoặc x = -1/3

ko phải e làm đâu nha a , a tham khảo cho 

a)CH4 + 2O2 →→ CO2 + 2H2O (1)

2H2 + O2 →→ 2H2O (2)

b) Đặt nCH4 = a (mol) , nH2 = b (mol)

=> mCH4 = 16a(g) , mH2 = 2b(g)

mà n(CH4 + H2) = V/22,4 = 6,72/22,4 = 0,3(mol)

=> a + b = 0,3(mol) => a = 0,3 - b

Từ PT(1) => nO2 = 2nCH4 = 2a(mol)

Từ PT(2) => nO2 = 1/2 . nH2 = 1/2 . b (mol)

=>tổng nO2 = 2a + 1/2.b (mol)

=> mO2 = n .M = 32. (2a+ 1/2.b )= 64a + 16b(g)

Theo ĐLBTKL:mCH4 + mH2 + mO2 = mCO2 + mH2O(PT1,2)

=> 16a + 2b+ 64a +16b = 11,6

=> 80a + 18b = 11,6

=> 80. (0,3 - b ) + 18b = 11,6

=> b = 0,2(mol)

=> a = 0,3 - 0,2 = 0,1(mol)

=>mCH4 = 16a = 16. 0,1 = 1,6(g) , mH2 = 2b = 2 . 0,2 = 0,4(g)

=> VCH4 = n .22,4 = 0,1 . 22,4 =2,24(l)

VH2 = n . 22,4 = 0,2 . 22,4 = 4,48(l)

tự tính ... 

c) nO2 = 2a + 1/2 .b = 2 . 0,1 + 1/2 . 0,2 = 0,3(mol)

=> VO2 = 0,3 . 22,4 =6,72(l)

mà VO2 = 20% Vkk

=> Vkk = 6,72 : 20% =33,6(l)