Question

giải phương trình 5-2x/3+(x-1)(x+1)/3x-1=(x+2)(1-3x)/9x-3

Answer 1

ĐKXĐ: \(x\ne\frac{1}{3}\)

Ta có: \(\frac{5-2x}{3}+\frac{\left(x-1\right)\left(x+1\right)}{\left(3x-1\right)}=\frac{\left(x+2\right)\left(1-3x\right)}{9x-3}\)

\(\Leftrightarrow\frac{\left(5-2x\right)\left(3x-1\right)}{3\left(3x-1\right)}+\frac{3\left(x^2-1\right)}{3\left(3x-1\right)}-\frac{\left(x+2\right)\left(1-3x\right)}{3\left(3x-1\right)}=0\)

\(\Leftrightarrow-6x^2+17x-5+3x^2-3-\left(-3x^2-5x+2\right)=0\)

\(\Leftrightarrow-3x^2+17x-8+3x^2+5x-2=0\)

\(\Leftrightarrow22x-10=0\)

\(\Leftrightarrow22x=10\)

hay \(x=\frac{5}{11}\)(tm)

Vậy: \(x=\frac{5}{11}\)