Question

[Dragneel Quốc Việt]

A)\(\left(x-11\right)+\frac{3x}{x-11}=3+\frac{33}{x-11}\)

B)\(\frac{7-2x}{x-1}=\frac{1-4x}{x+2}\)

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

D)\(\frac{109x-4}{111x+1}-1=0\)

E)\(\frac{x^2-7}{x}=x-\frac{1}{2}\)

F)\(\frac{x+1}{x+2}=3\)

Answer 1

[Cold Wind]

a) \(\left(x-11\right)+\frac{3x}{x-11}=3+\frac{33}{x-11}\)

\(\Leftrightarrow x+\frac{3x}{x-11}-\frac{33}{x-11}=14\)

\(\Leftrightarrow x^2-11x+3x-33=14x-154\)

\(\Leftrightarrow x^2-22x+121=0\)

\(\Leftrightarrow\left(x-11\right)^2=0\Leftrightarrow x=11\)

Vậy .......

b) \(\frac{7-2x}{x-1}=\frac{1-4x}{x+2}\Leftrightarrow\left(7-2x\right)\left(x+2\right)=\left(1-4x\right)\left(x-1\right)\)

\(\Leftrightarrow7x-2x^2+14-4x=x-4x^2-1+4x\)

\(\Leftrightarrow2x^2=-15\)(vô lí)

Vậy pt vô nghiệm

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

\(\Leftrightarrow\left(3-2x\right)\left(x-2\right)=2\left(x+1\right)\left(x-2\right)+\left(1-4x\right)\left(x+1\right)\)

\(\Leftrightarrow3x-2x^2-6x+4x=2x^2+2x-4x-4+x-4x^2+1-4x\)

\(\Leftrightarrow6x=-3\Leftrightarrow x=-\frac{1}{2}\)

Vậy.........

(gửi trước 3 câu)

Answer 2

[Cold Wind]

d) \(\frac{109x-4}{111x+1}-1=0\Leftrightarrow109x-4=111x+1\Leftrightarrow2x=-5\Leftrightarrow x=-\frac{5}{2}\)

Vậy x=-5/2

e) \(\frac{x^2-7}{x}=x-\frac{1}{2}\Leftrightarrow\frac{x^2-7}{x}-\frac{x^2}{x}=-\frac{1}{2}\Leftrightarrow-\frac{7}{x}=\frac{1}{2}\Leftrightarrow x=-14\)

f) \(\frac{x+1}{x+2}=3\Leftrightarrow x+1=3x+6\Leftrightarrow2x=7\Leftrightarrow x=\frac{7}{2}\)