A/  \(2\left(5x-3\right)=7x-18.\)

\(10x-6=7x-18\)

\(10-7x=6-18\)

\(3x=-12\)

\(x=-\frac{12}{3}=4\)

\(\Rightarrow S=\left\{4\right\}\)

B/  \(3x\left(x-2\right)+2x-4=0\)

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

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

\(\orbr{\begin{cases}x-2=0\Rightarrow x=2\\3x+2=0\Rightarrow3x=-2\Rightarrow x=-\frac{2}{3}\end{cases}}\)

\(\Rightarrow S=\left\{2;-\frac{2}{3}\right\}\)

C/  \(\frac{x+2}{3}\frac{x-3}{2}=\frac{x+5}{4}\)

\(\frac{\left(x+2\right)\left(x-3\right)}{3.2}=\frac{x+5}{4}\)

\(\frac{x^2-3x+2x-6}{6}=\frac{x+5}{4}\)

\(\frac{x^2-x-6}{6}=\frac{x+5}{4}\)

\(\frac{2\left(x^2-x-6\right)}{12}=\frac{3\left(x+5\right)}{12}\)

\(\frac{2x^2-2x-12}{12}=\frac{3x+15}{12}\)

\(\Rightarrow2x^2-2x-12=3x+15\)

(chuyển vế r làm tiếp)

Bài 1 : 

\(a,2\left(5x-3\right)=7x-18\)

\(\Leftrightarrow10x-6=7x-18\)

\(\Leftrightarrow10x-7x=6-18\)

\(\Leftrightarrow3x=-12\)

\(\Leftrightarrow x=-4\)

PT có nghiệm S = { -4 }

\(b,3x\left(x-2\right)+2x-4=0\)

\(\Leftrightarrow3x^2-6x+2x-4=0\)

\(\Leftrightarrow3x^2-4x-4=0\)

\(\Leftrightarrow3x^2-6x+2x-4=0\)

\(\Leftrightarrow3x\left(x-2\right)+2\left(x-2\right)=0\)

\(\Leftrightarrow\left(3x+2\right)\left(x-2\right)=0\)

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

KL : ............

\(c,\frac{x+2}{3}-\frac{x-3}{2}=\frac{x+5}{4}\)

\(\Leftrightarrow\frac{4\left(x+2\right)}{12}-\frac{6\left(x-3\right)}{12}=\frac{3\left(x+5\right)}{12}\)

\(\Leftrightarrow4x+8-6x+18=3x+15\)

\(\Leftrightarrow4x-6x-3x=-8-18+15\)

\(\Leftrightarrow x=-9\)

KL : .......

c/  \(\frac{5}{x-3}+\frac{2}{x-2}=\frac{5}{\left(x-3\right)\left(x-2\right)}.\)

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

\(\frac{5x-10}{\left(x-3\right)\left(x-2\right)}+\frac{2x-6}{\left(x-3\right)\left(x-2\right)}=\frac{5}{\left(x-3\right)\left(x-2\right)}\)

\(\frac{5x-10+2x-6}{\left(x-3\right)\left(x-2\right)}=\frac{5}{\left(x-3\right)\left(x-2\right)}\)

\(\frac{7x-16}{\left(x-3\right)\left(x-2\right)}=\frac{5}{\left(x-3\right)\left(x-2\right)}\)

\(\Rightarrow7x-16=5\)

\(\Rightarrow7x=5+16\)

\(\Rightarrow7x=21\)

\(\Rightarrow x=\frac{21}{7}=3\)

\(\Rightarrow S=\left\{3\right\}\)

D/ \(\frac{7x-2}{3}-2x< 5-\frac{x-2}{4}\)

\(\frac{7x-2}{3}-\frac{2x.3}{3}< \frac{5.4}{4}-\frac{x-2}{4}\)

\(\frac{7x-2}{3}-\frac{6x}{3}< \frac{20}{4}-\frac{x-2}{4}\)

\(\frac{7x-2-6x}{3}< \frac{20-x+2}{4}\)

\(\frac{x-2}{3}< \frac{22-x}{4}\)

\(\frac{4\left(x-2\right)}{12}< \frac{3\left(22-x\right)}{12}\)

\(\frac{4x-8}{12}< \frac{66-3x}{12}\)

\(\Rightarrow4x-8=66-3x\)

\(\Rightarrow4x+3x=66+8\)

\(\Rightarrow7x=74\)

\(\Rightarrow x=\frac{74}{7}\)

\(\Rightarrow S=\left\{\frac{74}{7}\right\}\)

i) (x - 1)(5x + 3) = (3x - 8)(x - 1)

<=> 5x² + 3x - 5x - 3 = 3x² - 3x - 8x + 8

<=> 5x² - 2x - 3 = 3x² - 11x + 8

<=> 5x² - 2x - 3 - 3x² + 11x - 8 = 0

<=> 2x² + 9x - 11 = 0

<=> 2x² + 11x - 2x - 11 = 0

<=> x(2x + 11) - (2x + 11) = 0

<=> (x - 1)(2x + 11) = 0

<=> x - 1 = 0 hoặc 2x + 11 = 0

<=> x = 0 hoặc x = -11/2

m) 2x(x - 1) = x² - 1

<=> 2x² - 2x = x² - 1

<=> 2x² - 2x - x² + 1 = 0

<=> x² - 2x + 1 = 0

<=> (x - 1)² = 0

<=> x - 1 = 0

<=> x = 1

n) (2 - 3x)(x + 11) = (3x - 2)(2 - 5x)

<=> 2x + 22 - 3x² - 33x = 6x - 15x² - 4 + 10x

<=> -31x + 22 - 3x² = 16x - 15x² - 4

<=> 31x - 22 + 3x² + 16x - 15x² - 4 = 0

<=> 47x - 18 - 12x² = 0

<=> -12x² + 47x - 26 = 0

<=> 12x² - 47x + 26 = 0

<=> 12x² - 8x - 39x + 26 = 0

<=> 4x(3x - 2) - 13(3x - 2) = 0

<=> (4x - 13)(3x - 2) = 0

<=> 4x - 13 = 0 hoặc 3x - 2 = 0

<=> x = 13/4 hoặc x = 2/3

i) (x - 1)(5x + 3) = (3x - 8)(x - 1)

<=> 5x² + 3x - 5x - 3 = 3x² - 3x - 8x + 8

<=> 5x² - 2x - 3 = 3x² - 11x + 8

<=> 5x² - 2x - 3 - 3x² + 11x - 8 = 0

<=> 2x² + 9x - 11 = 0

<=> 2x² + 11x - 2x - 11 = 0

<=> x(2x + 11) - (2x + 11) = 0

<=> (x - 1)(2x + 11) = 0

<=> x - 1 = 0 hoặc 2x + 11 = 0

<=> x = 0 hoặc x = -11/2

m) 2x(x - 1) = x² - 1

<=> 2x² - 2x = x² - 1

<=> 2x² - 2x - x² + 1 = 0

<=> x² - 2x + 1 = 0

<=> (x - 1)² = 0

<=> x - 1 = 0

<=> x = 1

n) (2 - 3x)(x + 11) = (3x - 2)(2 - 5x)

<=> 2x + 22 - 3x² - 33x = 6x - 15x² - 4 + 10x

<=> -31x + 22 - 3x² = 16x - 15x² - 4

<=> 31x - 22 + 3x² + 16x - 15x² - 4 = 0

<=> 47x - 18 - 12x² = 0

<=> -12x² + 47x - 26 = 0

<=> 12x² - 47x + 26 = 0

<=> 12x² - 8x - 39x + 26 = 0

<=> 4x(3x - 2) - 13(3x - 2) = 0

<=> (4x - 13)(3x - 2) = 0

<=> 4x - 13 = 0 hoặc 3x - 2 = 0

<=> x = 13/4 hoặc x = 2/3

wifi chán thế?

Đây là lớp 8 nha các b giúp mk với

Do mk viết nhầm

Đây là những bài cơ bản mà bạn!

\(\frac{5x-2}{3}=\frac{5-3x}{2}\)

\(< =>\frac{\left(5x-2\right).2}{6}=\frac{\left(5-3x\right).3}{6}\)

\(< =>\left(5x-2\right).2=\left(5-3x\right).3\)

\(< =>10x-4=15-9x\)

\(< =>10x+9x=15+4\)

\(< =>19x=19< =>x=1\)

\(\frac{10x+3}{12}=1+\frac{6+8x}{9}\)

\(< =>\frac{\left(10x+3\right).3}{36}=\frac{36}{36}+\frac{\left(6+8x\right).4}{36}\)

\(< =>\left(10x+3\right).3=36+\left(6+8x\right).4\)

\(< =>30x+9=36+24+32x\)

\(< =>32x-30x=9-36-24\)

\(< =>2x=9-60=-51< =>x=-\frac{51}{2}\)

ĐKXĐ : \(\hept{\begin{cases}x-2\ne0\\3-4x\ne0\end{cases}\Rightarrow\hept{\begin{cases}x\ne2\\x\ne\frac{3}{4}\end{cases}}}\)

\(\frac{5}{x-2}+\frac{6}{3-4x}=0\)

\(\frac{5\left(3-4x\right)}{\left(x-2\right)\left(3-4x\right)}+\frac{6\left(x-2\right)}{\left(3-4x\right)\left(x-2\right)}=0\)

\(15-20x+6x-12=0\)

\(3-14x=0\Leftrightarrow14x=3\Leftrightarrow x=\frac{3}{14}\)theo ĐKXĐ : x thỏa mãn 

a) Qui đồng rồi khử mẫu ta được:

   3(3x+2)-(3x+1)=2x.6+5.2

<=> 9x+6-3x-1 = 12x+10

<=> 9x-3x-12x  = 10-6+1

<=> -6x            = 5

<=> x               = -5/6

Vậy ....

b) ĐKXĐ: \(x\ne\pm2\)

Qui đồng rồi khử mẫu ta được:

   (x+1)(x+2)+(x-1)(x-2) = 2(x²+2)

<=> x²+3x+2+x²-3x+2 = 2x²+4

<=> x²+x²-2x²+3x-3x = 4-2-2

<=> 0x             = 0

<=> x vô số nghiệm

Vậy x vô số nghiệm với x khác 2 và x khác -2

c) \(\left(2x+3\right)\left(\frac{3x+7}{2-7x}+1\right)=\left(x-5\right)\left(\frac{3x+8}{2-7x}+1\right)\) (ĐKXĐ:x khắc 2/7)

\(\Leftrightarrow\left(2x+3\right)\left(\frac{3x+8}{2-7x}+1\right)-\left(x-5\right)\left(\frac{3x+8}{2-7x}+1\right)=0\)

\(\Leftrightarrow\left(\frac{3x+8}{2-7x}+1\right)\left[\left(2x+3\right)-\left(x-5\right)\right]=0\)

\(\Leftrightarrow\left(\frac{3x+8}{2-7x}+1\right)\left(x+8\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}\frac{3x+8}{2-7x}+1=0\\x+8=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}\frac{3x+8}{2-7x}=-1\\x+8=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}3x+8=-1\left(2-7x\right)\\x=0-8\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}3x+8=-2+7x\\x=-8\end{cases}\Leftrightarrow\orbr{\begin{cases}-4x=-10\\x=-8\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{5}{2}\\x=-8\end{cases}}}\) (nhận)

Vậy ...... 

d) (x+1)²-4(x²-2x+1) = 0

<=> x²+2x+1-4x²+8x-4 = 0

<=> -3x²+10x-3 = 0

giải phương trình