Question

BÀI 1: Giải phương trình sau:

a. (x - 4)³ = (x + 4)(x² - x - 16)

b. \(\dfrac{x+2}{x}=\dfrac{x^2+5x+4}{x^2+2x}+\dfrac{x}{x+2}\)

c. \(\dfrac{x+1}{x-2}-\dfrac{5}{x+2}=\dfrac{12}{x^2-4}+1\)

d. (x + 3)² - 25 = 0
e. \(\dfrac{3}{2x+10}+\dfrac{2x}{25-x^2}+\dfrac{3}{x-5}=0\)

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

BÀI 2: Tìm m để phương trình sau số nghiệm x = 1:

3.(2x + m)(x + 2) - 2.(2x+1) = 18

BÀI 3: Giải phương trình:

a. (x-2)² - 4.(x + 3) = x.(x-4)

b. \(\dfrac{3}{x+1}+\dfrac{x-1}{x-2}=\dfrac{x}{x-2}\)

c. \(\dfrac{x}{2x-6}+\dfrac{x}{2x+2}=\dfrac{2x^2}{x^2-2x-3}\)

d. (x + 3)² - (x - 3)² = 6x + 18

e. \(\dfrac{x+3}{x-2}=\dfrac{5}{\left(x-2\right)\left(3-x\right)}\)

f. \(\dfrac{12x^2+30x-21}{16x^2-9}-\dfrac{3x-7}{3-4x}=\dfrac{6x+5}{4x+3}\)

g. \(\dfrac{4}{x+1}-\dfrac{2}{x-2}=\dfrac{x+3}{x^2-x-2}\)

GIÚP MÌNH VỚI NHA !!!!

Answer 1

bài 1:

b,\(\dfrac{x+2}{x}=\dfrac{x^2+5x+4}{x^2+2x}+\dfrac{x}{x+2}\)(ĐKXĐ:x ≠0,x≠-2)

<=>\(\dfrac{\left(x+2\right)^2}{x\left(x+2\right)}=\dfrac{x^2+5x+4}{x\left(x+2\right)}+\dfrac{x^2}{x\left(x+2\right)}\)

=>\(x^2+4x+4=x^2+5x+4+x^2\)

<=>\(x^2-x^2-x^2+4x-5x+4-4=0\)

<=>\(-x^2-x=0< =>-x\left(x+1\right)=0< =>\left[{}\begin{matrix}x=0\left(loại\right)\\x+1=0< =>x=-1\left(nhận\right)\end{matrix}\right.\)

vậy...............

d,\(\left(x+3\right)^2-25=0< =>\left(x+3-5\right)\left(x+3+5\right)=0< =>\left(x-2\right)\left(x+8\right)=0< =>\left[{}\begin{matrix}x-2=0\\x+8=0\end{matrix}\right.< =>\left[{}\begin{matrix}x=2\\x=-8\end{matrix}\right.\)

vậy............

bài 3:

g,\(\dfrac{4}{x+1}-\dfrac{2}{x-2}=\dfrac{x+3}{x^2-x-2}\)(ĐKXĐ:x khác -1,x khác 2)

<=>\(\dfrac{4}{x+1}-\dfrac{2}{x-2}=\dfrac{x+3}{x^2-2x+x-2}\)

<=>\(\dfrac{4}{x+1}-\dfrac{2}{x-2}=\dfrac{x+3}{x\left(x-2\right)+\left(x-2\right)}\)

<=>\(\dfrac{4}{x+1}-\dfrac{2}{x-2}=\dfrac{x+3}{\left(x+1\right)\left(x-2\right)}\)

<=>\(\dfrac{4\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}-\dfrac{2\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}=\dfrac{x+3}{\left(x+1\right)\left(x-2\right)}\)

=>\(4x-8-2x-2=x+3\)

<=>\(x=13\)

vậy..............

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