Question

Giải các phương trình:

\(a,\frac{3}{2x-16}+\frac{3x-20}{x-8}+\frac{1}{8}=\frac{13x-102}{3x-24}\)

\(b,\frac{x-1}{x+2}-\frac{x}{x-2}=\frac{5x-2}{4-x^2}\)

Answer 1

Lời giải:
a) ĐKXĐ: $x\neq \pm 3; x\neq 0$

\(A=\frac{3-x}{x+3}.\frac{(x+3)^2}{(x-3)(x+3)}.\frac{x+3}{3x^2}\)

\(=-\frac{x+3}{3x^2}\)

b)

Với $x=-\frac{1}{2}\Rightarrow A=-\frac{-\frac{1}{2}+3}{3(\frac{-1}{2})^2}=\frac{-10}{3}$

c)

Để $A< 0\Leftrightarrow -\frac{x+3}{3x^2}< 0$

$\Rightarrow x+3>0\Rightarrow x>-3$

Vậy $x>-3; x\neq 3; x\neq 0$

Answer 2

Lời giải:

a) ĐK: $x\neq 8$

PT \(\Leftrightarrow \frac{3}{2(x-8)}+\frac{3x-20}{x-8}+\frac{1}{8}=\frac{13x-102}{3(x-8)}\)

\(\Leftrightarrow \frac{36}{24(x-8)}+\frac{24(3x-20)}{24(x-8)}+\frac{3(x-8)}{24(x-8)}=\frac{8(13x-102)}{24(x-8)}\)

\(\Rightarrow 36+24(3x-20)+3(x-8)=8(13x-102)\)

\(\Leftrightarrow x=12\) (t/m)

b)

ĐK: $x\neq \pm 2$

PT \(\Leftrightarrow \frac{(x-1)(x-2)}{(x+2)(x-2)}-\frac{x(x+2)}{(x-2)(x+2)}=\frac{5x-2}{(2-x)(x+2)}=\frac{2-5x}{(x-2)(x+2)}\)

\(\Rightarrow (x-1)(x-2)-x(x+2)=2-5x\)

$\Leftrightarrow 0=0$

Vậy PT có nghiệm $x\in\mathbb{R}$ và $x\neq \pm 2$