Question

a.4 / x+1 = 3 /x-2

b.x+2 / 2x-4 - 4x / x^2-4=0

c. 1 / x-3 -5/x = 3x+7 / x(x-3)

Answer 1

a, đk : x khác -1 ; x khác 2 

\(\Rightarrow4x-8=3x+3\Leftrightarrow x=11\left(tm\right)\)

b, đk : x khác 2 ; -2 

\(\Rightarrow\left(x+2\right)^2-8x=0\Leftrightarrow\left(x-2\right)^2=0\Leftrightarrow x=2\left(ktm\right)\)

-> vậy pt vô nghiệm 

c, đk : x khác 3  ; 0 

\(\Rightarrow x-5\left(x-3\right)=3x+7\Leftrightarrow-4x+15=3x+7\Leftrightarrow-7x=-8\Leftrightarrow x=\dfrac{8}{7}\left(tm\right)\)

 

Answer 2

a)Với \(x\ne-1;x\ne2\)

\(\dfrac{4}{x+1}=\dfrac{3}{x-2}\)

<=>4(x-2)=3(x+1)

<=>4x-8=3x+3

<=>x=11(TM)

b)Với\(x\ne\pm2\)

\(\dfrac{x+2}{2x-4}-\dfrac{4x}{x^2-4}=0\)

<=>\(\dfrac{x+2}{2\left(x-2\right)}-\dfrac{4x}{\left(x+2\right)\left(x-2\right)}=0\)

<=>\(\dfrac{\left(x+2\right)^2-8x}{2\left(x+2\right)\left(x-2\right)}=0\)

<=>\(x^2+4x+4-8x=0\left(Vĩx\ne\pm2\right)\)

<=>\(x^2-4x+4=0\)

<=>\(\left(x-2\right)^2=0\)

<=>x-2=0

<=>x=2(Không thỏa mãn)

c)Với \(x\ne3,x\ne0\)

\(\dfrac{1}{x-3}-\dfrac{5}{x}=\dfrac{3x+7}{x\left(x-3\right)}\)

<=>\(\dfrac{x-5\left(x-3\right)}{x\left(x-3\right)}=\dfrac{3x+7}{x\left(x-3\right)}\)

<=>x-5x+15=3x+7(Vì \(x\ne0,x\ne3\))

<=>7x=8

<=>x=\(\dfrac{8}{7}\left(TM\right)\)