Question

Giải pt: \(\dfrac{x-5}{x+6}-\dfrac{2x^2+23x+61}{x^2+x-30}=\dfrac{x+6}{5-x}\)

Answer 1

\(\dfrac{x-5}{x+6}-\dfrac{2x^2+23x+61}{x^2+x-30}=\dfrac{x+6}{5-x}\)(ĐKXĐ: \(x\notin\left\{5;-6\right\}\))

=>\(\dfrac{x-5}{x+6}-\dfrac{2x^2+23x+61}{\left(x+6\right)\left(x-5\right)}=\dfrac{-\left(x+6\right)}{x-5}\)

=>\(\dfrac{\left(x-5\right)^2-2x^2-23x-61}{\left(x+6\right)\left(x-5\right)}=\dfrac{-\left(x+6\right)^2}{\left(x-5\right)\left(x+6\right)}\)

=>\(x^2-10x+25-2x^2-23x-61=-x^2-12x-36\)

=>-33x-36=-12x-36

=>-21x=0

=>x=0(nhận)