Question

Giải pt

\(\frac{y-1}{y-2}-\frac{5}{y+2}=\frac{12}{y^2-4}+1\)

Answer 1

$\frac{y-1}{y-2}-\frac{5}{y+2}=\frac{12}{y^2-4}+1$

ĐKXĐ: \(x\ne2;x\ne-2\)

\(\Leftrightarrow\frac{y-1}{y-2}-\frac{5}{y+2}-\frac{12}{\left(y-2\right)\left(y+2\right)}-1=0\)

\(\Leftrightarrow\frac{\left(y-1\right)\left(y+2\right)-5\left(y-2\right)-12-\left(y-2\right)\left(y+2\right)}{\left(y-2\right)\left(y+2\right)}=0\)

\(\Leftrightarrow y^2+2y-y-2-5y+10-12-y^2-2y+2y+4=0\)

\(\Leftrightarrow-4y=0\)

\(\Leftrightarrow y=0\left(TM\right)\)

Vậy S = {0}