Question

[Julian Edward]

giải các phương trình chứa ẩn ở mẫu sau đây dạng \(\frac{p\left(x\right)}{q\left(x\right)}-\frac{r\left(x\right)}{h\left(x\right)}=a\)

a) \(\frac{5x-1}{3x+2}=\frac{5x-7}{3x-1}\)

b) \(\frac{4x+7}{x-1}=\frac{12x+5}{3x+4}\)

c) \(\frac{3\left(x^2-1\right)}{4x+1}+\frac{2}{x}-2x=x^2-1\)

Mn giup e vs ah, thenk kiu :3333

Answer 1

[Nguyễn Việt Lâm]

a/ ĐKXĐ: \(x\ne\left\{-\frac{2}{3};\frac{1}{3}\right\}\)

\(\Leftrightarrow\left(5x-1\right)\left(3x-1\right)=\left(5x-7\right)\left(3x+2\right)\)

\(\Leftrightarrow15x^2-8x+1=15x^2-11x-14\)

\(\Leftrightarrow3x=-15\Rightarrow x=-5\)

b/ ĐKXĐ: \(x\ne\left\{-\frac{4}{3};1\right\}\)

\(\Leftrightarrow\left(4x+7\right)\left(3x+4\right)=\left(12x+5\right)\left(x-1\right)\)

\(\Leftrightarrow12x^2+37x+28=12x^2-7x-5\)

\(\Leftrightarrow44x=-33\Rightarrow x=-\frac{3}{4}\)

c/ ĐKXĐ: \(x\ne\left\{-\frac{1}{4};0\right\}\)

\(\Leftrightarrow\frac{3\left(x^2-1\right)}{4x+1}+\frac{2\left(1-x^2\right)}{x}-\left(x^2-1\right)=0\)

\(\Leftrightarrow\left(x^2-1\right)\left(\frac{3}{4x+1}-\frac{2}{x}-1\right)=0\)

TH1: \(x^2-1=0\Rightarrow x=\pm1\)

TH2: \(\frac{3}{4x+1}-\frac{2}{x}-1=0\Leftrightarrow3x-2\left(4x+1\right)-x\left(4x+1\right)=0\)

\(\Leftrightarrow4x^2+6x+2=0\) \(\Rightarrow\left[{}\begin{matrix}x=-1\\x=-\frac{1}{2}\end{matrix}\right.\)

Answer 2

[Julian Edward]

thenk kiu :333