1, Đk x≠2;-2

\(\frac{x+2}{2x-4}-\frac{4x}{x^2-4}=0\\ =>\frac{x+2}{2\left(x-2\right)}-\frac{4x}{\left(x-2\right).\left(x+2\right)}=0\\ =>\frac{\left(x+2\right)^2}{2\left(x^2-4\right)}-\frac{8x}{2\left(x-2\right).\left(x+2\right)}=0\\ =>\frac{x^2+4x+4-8x}{2\left(x-2\right)\left(x+2\right)}=0\\ =>\frac{x^2-4x+4}{2\left(x-2\right)\left(x+2\right)}=0\\ =>\frac{x-2}{2\left(x+2\right)}=0\\ =>x-2=0\\ =>x=2\left(loại\right)\)

       \(2x-2=8-3x\)

\(\Leftrightarrow\)\(2x+3x=8+2\)

\(\Leftrightarrow\)\(5x=10\)

\(\Leftrightarrow\)\(x=2\)

Vậy...

         \(x^2-3x+1=x+x^2\)

\(\Leftrightarrow\)\(x^2-3x-x-x^2=-1\)

\(\Leftrightarrow\)\(-4x=-1\)

\(\Leftrightarrow\)\(x=\frac{1}{4}\)

Vậy...

mấy cái này bấm máy tính là đc òi. giải mất thời gian lắm :))

\(2x-2=8-3x\)

\(\Leftrightarrow\)\(2x+3x=8+2\)

\(\Leftrightarrow\)\(5x=10\)

\(\Leftrightarrow\)\(x=2\)

Vậy \(x=2\)

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

\(\Leftrightarrow\)\(4x-1=\left(x^2+x\right)-\left(x^2+x\right)\)

\(\Leftrightarrow\)\(4x-1=0\)

\(\Leftrightarrow\)\(4x=1\)

\(\Leftrightarrow\)\(x=\frac{1}{4}\)

Vậy \(x=\frac{1}{4}\)

\(\left(x^2+1\right)\left(2x+4\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x^2+1=0\\2x+4=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x^2=-1\\2x=-4\end{cases}}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=\sqrt{-1}\\x=\frac{-4}{2}\end{cases}\Leftrightarrow\orbr{\begin{cases}x\in\left\{\varnothing\right\}\\x=-2\end{cases}}}\)

Vậy \(x=-2\)

Chúc bạn học tốt ~ 

\(ĐKXĐ:x\ne3;x\ne5;x\ne4;x\ne6\)

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

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

\(\Rightarrow x\left(\frac{1}{x-3}-\frac{1}{x-5}-\frac{1}{x-4}+\frac{1}{x-6}\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x=0\left(tm\right)\\\frac{1}{x-3}-\frac{1}{x-5}-\frac{1}{x-4}+\frac{1}{x-6}=0\left(1\right)\end{cases}}\)

\(\left(1\right)\Rightarrow\frac{1}{x-3}+\frac{1}{x-6}=\frac{1}{x-5}+\frac{1}{x-4}\)

\(\Rightarrow\frac{2x-9}{\left(x-3\right)\left(x-6\right)}=\frac{2x-9}{\left(x-5\right)\left(x-4\right)}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{9}{2}\left(tm\right)\\\left(x-3\right)\left(x-6\right)=\left(x-5\right)\left(x-4\right)\left(2\right)\end{cases}}\)

\(\left(2\right)\Leftrightarrow x^2-9x+18=x^2-9x+20\)

\(\Leftrightarrow0=2\left(L\right)\)

Vậy pt có 2 nghiệm \(\left\{0;\frac{9}{2}\right\}\)

1/ Đặt \(\sqrt{9-x^2}=a\ge0\)

\(\Rightarrow\frac{9-a^2}{3+a}+\frac{1}{12-4a}=1\)

\(\Leftrightarrow4a^2-20a+25=0\)

\(\Leftrightarrow a=\frac{5}{2}\)

\(\Rightarrow\sqrt{9-x^2}=\frac{5}{2}\)

\(\Leftrightarrow x^2=\frac{11}{4}\)

\(\Leftrightarrow\orbr{\begin{cases}x=-\frac{\sqrt{11}}{2}\\x=\frac{\sqrt{11}}{2}\end{cases}}\)

2/ \(\frac{9}{x^2}+\frac{2x}{\sqrt{2x^2+9}}-1=0\)

\(\Leftrightarrow\frac{9+2x^2}{x^2}+\frac{2x}{\sqrt{2x^2+9}}-3=0\)

Đặt \(\frac{x}{\sqrt{2x^2+9}}=a\)

\(\Rightarrow\frac{1}{a^2}+2a-3=0\)

\(\Leftrightarrow2a^3-3a^2+1=0\)

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

Làm nốt nhé

3/ \(x+\frac{x}{\sqrt{x^2-1}}=2\sqrt{2}\)

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

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

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

\(\Leftrightarrow x=\sqrt{2}\)

1. \(\frac{7x-1}{6}+2x=\frac{16-x}{5}\)

\(\Leftrightarrow5\left(7x-1\right)+60x=6\left(16-x\right)\)

\(\Leftrightarrow35x-5+60x=96-6x\)

\(\Leftrightarrow95x-5=96-6x\)

\(\Leftrightarrow95x+6x=96+5\)

\(\Leftrightarrow101x=101\)

\(\Leftrightarrow x=1\)

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

\(\Leftrightarrow3\left(10x+3\right)=36+4\left(6+8x\right)\)

\(\Leftrightarrow30x+9=36+24+32x\)

\(\Leftrightarrow30x+9=32x+60\)

\(\Leftrightarrow30x-32x=60-9\)

\(\Leftrightarrow-2x=51\)

\(\Leftrightarrow x=-\frac{51}{2}\)

3. \(\frac{8x-3}{4}-\frac{3x-2}{2}=\frac{2x-1}{2}+\frac{x+3}{4}\)

\(\Leftrightarrow8x-3-2\left(3x-2\right)=2\left(2x-1\right)+x+3\)

\(\Leftrightarrow8x-3-6x+4=4x-2+x+3\)

\(\Leftrightarrow2x+1=5x+1\)

\(\Leftrightarrow2x=5x\)

\(\Leftrightarrow x=0\)

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

=> \(\frac{9-3x}{8}+\frac{10-2x}{3}=\frac{1-x}{2}-\frac{2}{1}\)

=> \(\frac{3\left(9-3x\right)}{24}+\frac{8\left(10-2x\right)}{24}=\frac{12\left(1-x\right)}{24}-\frac{48}{24}\)

=> \(\frac{27-9x}{24}+\frac{80-16x}{24}=\frac{12-12x}{24}-\frac{48}{24}\)

=> \(\frac{27-9x+80-16x}{24}=\frac{12-12x-48}{24}\)

=> 27 - 9x + 80 - 16x = 12 - 12x - 48

=> 27 - 9x + 80 - 16x - 12 + 12x + 48 = 0

=> (27 + 80 - 12 + 48) + (-9x - 16x + 12x) = 0

=> 143 - 13x = 0

=> 13x = 143

=> x = 11

5) \(\frac{2\left(x-3\right)}{7}+\frac{x-5}{3}-\frac{13x+4}{21}=0\)

=> \(\frac{2x-6}{7}+\frac{x-5}{3}-\frac{13x+4}{21}=0\)

=> \(\frac{3\left(2x-6\right)}{21}+\frac{7\left(x-5\right)}{21}-\frac{13x+4}{21}=0\)

=> \(\frac{6x-18}{21}+\frac{7x-35}{21}-\frac{13x+4}{21}=0\)

=> \(\frac{6x-18+7x-35-13x-4}{21}=0\)

=> 6x - 18 + 7x - 35 - 13x - 4 = 0

=> (6x + 7x - 13x) + (-18 - 35 - 4) = 0

=> -57 = 0(vô nghiệm)

6) \(\frac{6x+5}{2}-\left(2x+\frac{2x+1}{2}\right)=\frac{10x+3}{4}\)

=> \(\frac{6x+5}{2}-\frac{10x+3}{4}=2x+\frac{2x+1}{2}\)

=> \(\frac{2\left(6x+5\right)}{4}-\frac{10x+3}{4}=\frac{8x}{4}+\frac{2\left(2x+1\right)}{4}\)

=> \(\frac{12x+10}{4}-\frac{10x+3}{4}=\frac{8x}{4}+\frac{4x+2}{4}\)

=> \(\frac{12x+10-\left(10x+3\right)}{4}=\frac{8x+4x+2}{4}\)

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

=> \(12x+10-10x-3=12x+2\)

=> \(2x+10-3=12x+2\)

=> 2x + 10 - 3 - 12x - 2 = 0

=> (2x - 12x) + (10 - 3 - 2) = 0

=> -10x + 5 = 0

=> -10x = -5

=> x = 1/2

7) \(\frac{2x-1}{5}-\frac{x-2}{3}-\frac{x+7}{15}=0\)

=> \(\frac{3\left(2x-1\right)}{15}-\frac{5\left(x-2\right)}{15}-\frac{x+7}{15}=0\)

=> \(\frac{6x-3}{15}-\frac{5x-10}{15}-\frac{x+7}{15}=0\)

=> \(\frac{6x-3-\left(5x-10\right)-\left(x+7\right)}{15}=0\)

=> 6x - 3 - 5x + 10 - x - 7 = 0

=> (6x - 5x - x) + (-3 + 10 - 7) = 0

=> 0x + 0 = 0

=> 0x = 0

=> x tùy ý

Bài 8 tự làm nhé

\(\frac{-5}{9}x+1=\frac{2}{3}x-10\)

\(\frac{-5}{9}x+\frac{9}{9}=\frac{6}{9}x-\frac{90}{9}\)

\(-5x+9=6x-90\)

\(-5x-6x=-90-9\)

\(-11x=-99\)

\(x=\frac{-99}{-11}=9\)

b. \(\frac{x-22}{8}+\frac{x-21}{9}+\frac{x-20}{10}+\frac{x-19}{11}=4\)

\(\frac{x-22}{8}-1+\frac{x-21}{9}-1+\frac{x-20}{10}-1+\frac{x-19}{11}-1=0\)

\(\frac{x-30}{8}+\frac{x-30}{9}+\frac{x-30}{10}+\frac{x-30}{11}=0\)

\(\left(x-30\right)\left(\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}\right)=0\)

x=30

Chúc bạn học tốt!!