Question

giải phương trình \(\dfrac{1}{x+1}-\dfrac{5}{x-2}=\dfrac{15}{\left(x-1\right)\left(2-x\right)}\)

Answer 1

 

⇔1x+1+52−x=15(x+1)(2−x)⇔1x+1+52−x=15(x+1)(2−x)

$\iff 2-x+5x+5=15$

$\iff 4x+7=15$

$\iff 4x=8$

Answer 2

ĐKXĐ : \(\left\{{}\begin{matrix}x\ne\pm1\\x\ne2\end{matrix}\right.\)

PT \(\Leftrightarrow\dfrac{\left(x-2\right)\left(x-1\right)}{\left(x+1\right)\left(x-1\right)\left(x-2\right)}-\dfrac{5\left(x+1\right)\left(x-1\right)}{\left(x-2\right)\left(x+1\right)\left(x-1\right)}=\dfrac{-15\left(x+1\right)}{\left(x+1\right)\left(x-1\right)\left(x-2\right)}\)\(\Leftrightarrow\left(x-2\right)\left(x-1\right)-5\left(x+1\right)\left(x-1\right)=-15\left(x+1\right)\)

\(\Leftrightarrow x^2-2x-x+2-5x^2+5=-15x-15\)

\(\Leftrightarrow x^2-2x-x+2-5x^2+5+15x+15=0\)

\(\Leftrightarrow-4x^2+12x+22=0\)

\(\Leftrightarrow x=\dfrac{3\pm\sqrt{31}}{2}\) ( TM )

Vậy ...

 

Answer 3

Lag v :vvv