Question

Giải các phương trình sau:

A) 1/x-2+3=3-x/x-2

B)8-x/x-7-8=-26/x-7

C)1/x-2+1/x-3=2/x-1

D)X^3-1/X=(x-2)(x+2)+11/x

E)x+5/x-5-x-5/x+5=20/x^2-25

F)x+7/x-3+4x-2/x-5=5

Answer 1

a: \(\dfrac{1}{x-2}+3=\dfrac{3-x}{x-2}\)

=>1+3x-6=3-x

=>3x-5=3-x

=>4x=8

hay x=2(loại)

b: \(\Leftrightarrow8-x-8\left(x-7\right)=-26\)

=>8-x-8x+56=-26

=>-9x+64=-26

=>-9x=-90

hay x=10(nhận)

c: \(\dfrac{1}{x-2}+\dfrac{1}{x-3}=\dfrac{2}{x-1}\)

\(\Leftrightarrow\dfrac{x-3+x-2}{\left(x-2\right)\left(x-3\right)}=\dfrac{2}{x-1}\)

\(\Leftrightarrow\left(x-1\right)\left(2x-5\right)=2\left(x^2-5x+6\right)\)

\(\Leftrightarrow2x^2-5x-2x+5=2x^2-10x+12\)

=>-7x+10x=12-5

=>3x=7

hay x=7/3(nhận)