a)
`(3x-1)/4+(6x-5)/8=(1-3x)/6`
`<=>18x-6+18x-15=4-12x`
`<=>18x+18x+12x=4+6+15`
`<=>48x=25`
`<=>x=25/48`
b)
`(1-2x)^2 +(x-3)(2x-1)=0`
`<=>1-4x+4x^2 +2x^2 -x-6x+3=0`
`<=>4x^2 +2x^2 -4x-x-6x+1+3=0`
`<=>6x^2 -11x+4=0`
`<=>6x^2 -3x-8x+4=0`
`<=>3x(2x-1)-4(2x-1)=0`
`<=>(3x-4)(2x-1)=0`
`<=>3x-4=0` hoặc `2x-1=0`
`<=>x=4/3` hoặc `x=1/2`
c)
\(\dfrac{1}{x-1}+\dfrac{2x^2-5}{x^3-1}=\dfrac{4}{x^2+x+1}\left(x\ne1\right)\)
`<=>(x^2 +x+1)/((x-1)(x^2 +x+1))+(2x^2 -5)/((x-1)(x^2 +x+1))=(4(x-1))/((x-1)(x^2 +x+1))`
Suy ra
`x^2 +x+1+2x^2 -5=4x-4`
`<=>x^2 +2x^2 +x-4x-5+1+4=0`
`<=>3x^2 -3x=0`
`<=>3x(x-1)=0`
`<=>3x=0` hoặc `x-1=0`
`<=>x=0(tm)` hoặc `x=1(ktm)`
\(1.\)
\(a.\dfrac{3x-1}{4}+\dfrac{6x-5}{8}=\dfrac{1-3x}{6}\)
\(\Leftrightarrow\dfrac{12\left(3x-1\right)}{48}+\dfrac{6\left(6x-5\right)}{48}=\dfrac{8\left(1-3x\right)}{48}\)
\(\Leftrightarrow12\left(3x-1\right)+6\left(6x-5\right)=8\left(1-3x\right)\)
\(\Leftrightarrow36x-12+36x-30=8-24x\)
\(\Leftrightarrow36x-12+36x-30-8+24x=0\)
\(\Leftrightarrow96x-50=0\)
\(\Leftrightarrow x=\dfrac{50}{96}=\dfrac{25}{48}\)
\(b.\left(1-2x\right)^2+\left(x-3\right)\left(2x-1\right)=0\)
\(\Leftrightarrow1^2+4x-2x^2+2x^2-x-6x+3=0\)
\(\Leftrightarrow1+4x-x-6x+3=0\)
\(\Leftrightarrow-3x+4=0\)
\(\Leftrightarrow x=\dfrac{-4}{3}\)
