Question

Giải phương trình:

a)\(\dfrac{x-3}{x+3}-\dfrac{x+3}{x-3}=\dfrac{48}{x^2-9}\)

b)\(\dfrac{x-5}{x-1}=\dfrac{2x-3}{x^2-1}+\dfrac{x}{x+1}\)

Answer 1

\(a,\Leftrightarrow\dfrac{\left(x-3\right)^2-\left(x+3\right)^2-48}{x^2-9}=0\)

\(\Leftrightarrow x^2-6x+9-x^2-6x-9-48=0\)

\(\Leftrightarrow-12x-48=0\)

\(\Leftrightarrow-12x=48\)

\(\Leftrightarrow x=-4\)

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

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

\(\Leftrightarrow-5x-8=0\)

\(\Leftrightarrow-5x=8\)

\(\Leftrightarrow x=-\dfrac{8}{5}\)