Question

Giải phương trình:[(x+1)/(x-2)]^2+[(x+1)/(x-3)]=12[(x-2)/(x-3)]^2

Answer 1

\(\left(\dfrac{x+1}{x-2}\right)^2+\dfrac{x+1}{x-3}=12\cdot\left(\dfrac{x-2}{x-3}\right)^2\) (ĐKXĐ: \(x\ne2;x\ne3\))

\(\Leftrightarrow\dfrac{\left(x+1\right)^2}{\left(x-2\right)^2}+\dfrac{x+1}{x-3}=\dfrac{12\left(x-2\right)^2}{\left(x-3\right)^2}\)

\(\Leftrightarrow\dfrac{\left(x-3\right)\left(x+1\right)^2+\left(x+1\right)\left(x-2\right)^2}{\left(x-2\right)^2\left(x-3\right)^2}=\dfrac{12\left(x-2\right)^4}{\left(x-2\right)^2\left(x-3\right)^2}\)