Question

B1 : Giải phương trình

a. \(\dfrac{x-2}{x-4}-\dfrac{1}{x-2}=-2\)

b. \(\dfrac{x-2}{x+3}-\dfrac{x+1}{3-x}=\dfrac{2x^2+6}{x^2-9}\)

c. \(\dfrac{2x-1}{3}-\dfrac{x-6}{4}=\dfrac{3x-2}{2}\)

d. \(\dfrac{3x-1}{4}+\dfrac{8x-21}{20}=\dfrac{3\left(x+2\right)}{5}-2\)

Answer 1

Answer 2

a: \(\Leftrightarrow x^2-4-x+4=-2\left(x^2-6x+8\right)\)

=>-2x^2+12x-16=x^2-x

=>-3x^2+13x-16=0

=>3x^2-13x+16=0

Δ=(-13)^2-4*3*16=169-192<0

=>PTVN
b: \(\Leftrightarrow\left(x-2\right)\left(x-3\right)+\left(x+1\right)\left(x+3\right)=2x^2+6\)

=>x^2-5x+6+x^2+4x+3=2x^2+6

=>-x+9=6

=>-x=-3

=>x=3(loại)

c: \(\Leftrightarrow4\left(2x-1\right)-3\left(x-6\right)=6\left(3x-2\right)\)

=>8x-4-3x+12=18x-12

=>-5x+8=18x-12

=>-23x=-20

=>x=20/23

d: \(\Leftrightarrow5\left(3x-1\right)+8x-21=12\left(x+2\right)-40\)

=>15x-5+8x-21=12x+24-40

=>23x-26=12x-16

=>11x=10

=>x=10/11