Question

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Giúp mình giải hộ bài 7 với Ai giúp mình được mình sẽ thả ❤️❤️ Cho

Answer 1

[Nguyễn Lê Phước Thịnh]

Bài 7:

a: ĐKXĐ: \(x\notin\left\{\dfrac{1}{2};-5\right\}\)

\(\dfrac{x+5}{2x-1}-\dfrac{1-2x}{x+5}-2=0\)

=>\(\dfrac{x+5}{2x-1}+\dfrac{2x-1}{x+5}-2=0\)

=>\(\dfrac{\left(x+5\right)^2+\left(2x-1\right)^2}{\left(2x-1\right)\left(x+5\right)}=2\)

=>\(\left(x+5\right)^2+\left(2x-1\right)^2=2\left(2x-1\right)\left(x+5\right)\)

=>\(x^2+10x+25+4x^2-4x+1=2\left(2x^2+10x-x-5\right)\)

=>\(5x^2+6x+26-4x^2-18x+10=0\)

=>\(x^2-12x+36=0\)

=>\(\left(x-6\right)^2=0\)

=>x-6=0

=>x=6(nhận)

b: ĐKXĐ: \(x\notin\left\{3;-2;4\right\}\)

\(1-\dfrac{8}{x-4}=\dfrac{5}{3-x}-\dfrac{8-x}{x+2}\)

=>\(\dfrac{x-4-8}{x-4}=\dfrac{-5}{x-3}+\dfrac{x-8}{x+2}\)

=>\(\dfrac{x-12}{x-4}=\dfrac{-5\left(x+2\right)+\left(x-8\right)\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}\)

=>\(\dfrac{x-12}{x-4}=\dfrac{-5x-10+x^2-11x+24}{\left(x-3\right)\left(x+2\right)}\)

=>\(\left(x-12\right)\left(x^2-x-6\right)=\left(x-4\right)\left(x^2-16x+14\right)\)

=>\(x^3-x^2-6x-12x^2+12x+72=x^3-16x^2+14x-4x^2+64x-56\)

=>\(-13x^2+6x+72=-20x^2+78x-56\)

=>\(7x^2-72x+128=0\)

=>\(\left[{}\begin{matrix}x=8\left(nhận\right)\\x=\dfrac{16}{7}\left(nhận\right)\end{matrix}\right.\)

c: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)

\(\dfrac{x-1}{x+2}+\dfrac{2}{x-2}=\dfrac{12}{x^2-4}\)

=>\(\dfrac{x-1}{x+2}+\dfrac{2}{x-2}=\dfrac{12}{\left(x-2\right)\left(x+2\right)}\)

=>\(\dfrac{\left(x-1\right)\left(x-2\right)+2\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}=\dfrac{12}{\left(x-2\right)\left(x+2\right)}\)

=>\(x^2-3x+2+2x+4=12\)

=>\(x^2-x-6=0\)

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

=>\(\left[{}\begin{matrix}x=3\left(nhận\right)\\x=-2\left(loại\right)\end{matrix}\right.\)