Question

Giải phương trình:

a)\(\dfrac{3x+2}{3x-2}\)\(-\)\(\dfrac{6}{2+3x}\)\(=\)\(\dfrac{9x^2}{9x^2-4}\)

b)\(\dfrac{5-x}{4x^2-8x}\)+\(\dfrac{7}{8x}\)=\(\dfrac{x-1}{2x\left(x-2\right)}\)+\(\dfrac{1}{8x-16}\)

Answer 1

a)\(\dfrac{3x+2}{3x-2}-\dfrac{6}{2+3x}=\dfrac{9x^2}{9x^2-4}\left(ĐKXĐ:x\ne\pm\dfrac{2}{3}\right)\)

\(\Leftrightarrow\dfrac{3x+2}{3x-2}-\dfrac{6}{3x+2}=\dfrac{9x^2}{\left(3x-2\right)\left(3x+2\right)}\)

\(\Leftrightarrow\dfrac{\left(3x+2\right)^2-6\left(3x-2\right)}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{9x^2}{\left(3x-2\right)\left(3x+2\right)}\)

\(\Rightarrow9x^2+12x+4-18x+12=9x^2\)

\(\Leftrightarrow9x^2-6x+16-9x^2=0\)

\(\Leftrightarrow-6x=-16\)

\(\Leftrightarrow x=\dfrac{8}{3}\) (thỏa mãn ĐKXĐ)

Vậy .................

Answer 2

b) \(\dfrac{5-x}{4x^2-8x}+\dfrac{7}{8x}=\dfrac{x-1}{2x\left(x-2\right)}+\dfrac{1}{8x-16}\left(ĐKXĐ:x\ne0;x\ne2\right)\)

\(\Leftrightarrow\dfrac{5-x}{4x\left(x-2\right)}+\dfrac{7}{8x}=\dfrac{x-1}{2x\left(x-2\right)}+\dfrac{1}{8\left(x-2\right)}\)

\(\Leftrightarrow\dfrac{2\left(5-x\right)+7\left(x-2\right)}{8x\left(x-2\right)}=\dfrac{4\left(x-1\right)+x}{8x\left(x-2\right)}\)

\(\Rightarrow10-2x+7x-14=4x-4+x\)

\(\Leftrightarrow5x-4=5x-4\)

\(\Leftrightarrow0x=0\) (vô số nghiệm)

Vậy \(S=R\backslash\left\{0;2\right\}\)