1: ĐKXĐ: x<>1/2

Ta có: \(\frac{2x-1}{4}=\frac{4}{2x-1}\)

=>\(\left(2x-1\right)\left(2x-1\right)=4\cdot4\)

=>\(\left(2x-1\right)^2=16\)

=>\(\left[\begin{array}{l}2x-1=4\\ 2x-1=-4\end{array}\right.\Rightarrow\left[\begin{array}{l}2x=4+1=5\\ 2x=-4+1=-3\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac52\left(nhận\right)\\ x=-\frac32\left(nhận\right)\end{array}\right.\)

2: ĐKXĐ: x<>1/2

\(\frac{2x-1}{27}=\frac{3}{2x-1}\)

=>\(\left(2x-1\right)\left(2x-1\right)=27\cdot3=81\)

=>\(\left(2x-1\right)^2=81\)

=>\(\left[\begin{array}{l}2x-1=9\\ 2x-1=-9\end{array}\right.\Rightarrow\left[\begin{array}{l}2x=10\\ 2x=-8\end{array}\right.\Rightarrow\left[\begin{array}{l}x=5\left(nhận\right)\\ x=-4\left(nhận\right)\end{array}\right.\)

3: ĐKXĐ: x∉{0;-1}

Ta có: \(\frac{4}{x}=\frac{8}{x+1}\)

=>\(\frac{1}{x}=\frac{2}{x+1}\)

=>2x=x+1

=>2x-x=1

=>x=1(nhận)

4: ĐKXĐ: x<>-5

Ta có: \(\frac{x-1}{x+5}=\frac67\)

=>7(x-1)=6(x+5)

=>7x-7=6x+30

=>7x-6x=7+30

=>x=37(nhận)

5: \(\frac{x-3}{5}=\frac{5-2x}{11}\)

=>11(x-3)=5(5-2x)

=>11x-33=25-10x

=>21x=25+33=58

=>\(x=\frac{58}{21}\)

6: ĐKXĐ: x∉{-1;-7}

Ta có: \(\frac{x}{x+1}=\frac{x+5}{x+7}\)

=>x(x+7)=(x+1)(x+5)

=>\(x^2+7x=x^2+6x+5\)

=>7x=6x+5

=>7x-6x=5

=>x=5(nhận)

7: ĐKXĐ: x∉{-2/5;-1/5}

ta có: \(\frac{2x+3}{5x+2}=\frac{4x+5}{10x+2}\)

=>(2x+3)(10x+2)=(5x+2)(4x+5)

=>\(20x^2+4x+30x+6=20x^2+25x+8x+10\)

=>34x+6=33x+10

=>34x-33x=10-6

=>x=4(nhận)

8: ĐKXĐ: x∉{-2;-8}

ta có: \(\frac{2x-18}{2x+4}=\frac{2x-17}{2x+16}\)

=>\(\frac{2\left(x-9\right)}{2\left(x+2\right)}=\frac{2x-17}{2x+16}\)

=>\(\frac{x-9}{x+2}=\frac{2x-17}{2x+16}\)

=>(2x-17)(x+2)=(x-9)(2x+16)

=>\(2x^2+4x-17x-34=2x^2+16x-9x-144\)

=>-13x-34=7x-144

=>-13x-7x=-144+34

=>-20x=-110

=>\(x=\frac{110}{20}=\frac{11}{2}\) (nhận)

tất cả các câu đều là tỉ lệ thức nhé