Question

Giải pt:

a)\(\dfrac{x+5}{2x-1}-\dfrac{1-2x}{x+5}-2=0\)

b)\(\dfrac{9x-27}{2x-7}-\dfrac{8x-28}{x-3}=0\)

c)\(\dfrac{2x+3}{x-3}-\dfrac{3\left(x-3\right)}{x+3}-2=0\)

Answer 1

a: \(\Leftrightarrow\dfrac{x+5}{2x-1}+\dfrac{2x-1}{x+5}-2=0\)

\(\Leftrightarrow\left(x+5\right)\left(x+5\right)+\left(2x-1\right)^2-2\left(2x-1\right)\left(x+5\right)=0\)

\(\Leftrightarrow x^2+10x+25+4x^2-4x+1-2\left(2x^2+10x-x-5\right)=0\)

\(\Leftrightarrow5x^2+6x+26-4x^2-18x+10=0\)

\(\Leftrightarrow x^2-12x+36=0\)

=>x=6

b: \(\dfrac{9x-27}{2x-7}-\dfrac{8x-28}{x-3}=0\)

\(\Leftrightarrow9\left(x-3\right)^2-4\left(2x-7\right)^2=0\)

\(\Leftrightarrow\left(3x-9\right)^2-\left(4x-14\right)^2=0\)

\(\Leftrightarrow\left(3x-9-4x+14\right)\left(3x-9+4x-14\right)=0\)

\(\Leftrightarrow\left(5-x\right)\left(7x-23\right)=0\)

hay \(x\in\left\{5;\dfrac{23}{7}\right\}\)