đề sai

phải không

?????????

k sai nhé 

\(\frac{x-1}{x^2-9x+20}+\frac{2x-2}{x^2-6x+8}+\frac{3x-3}{x^2-x-2}+\frac{4x-4}{x^2+6x+5}=0\)

\(\Leftrightarrow\frac{x-1}{\left(x-5\right)\left(x-4\right)}+\frac{2\left(x-1\right)}{\left(x-4\right)\left(x-2\right)}+\frac{3\left(x-1\right)}{\left(x-2\right)\left(x+1\right)}+\frac{4\left(x-1\right)}{\left(x+1\right)\left(x+5\right)}=0\)

\(\Leftrightarrow\left(x-1\right)\left(\frac{10}{x^2-25}\right)=0\)

\(\Leftrightarrow x-1=0\)

\(\Leftrightarrow x=1\)  

PS: Điều kiện xác đinh bạn tự làm nhé 

từ đề\(\Leftrightarrow\frac{x-1}{x\left(x-4\right)-5\left(x-4\right)}+\frac{2x-2}{x\left(x-2\right)-4\left(x-2\right)}+\frac{3x-3}{x\left(x+1\right)-2\left(x+1\right)}+\frac{4x-4}{x\left(x+1\right)+5\left(x+5\right)}=0\)

\(\Leftrightarrow\left(x-1\right)\left(\frac{1}{\left(x-4\right)\left(x-5\right)}+\frac{2}{\left(x-2\right)\left(x-4\right)}+\frac{3}{\left(x-2\right)\left(x+1\right)}+\frac{4}{\left(x+1\right)\left(x+5\right)}=0\right)\)

\(\Leftrightarrow\left(x-1\right)\left(\frac{1}{x-4}-\frac{1}{x-5}+\frac{1}{x-2}-\frac{1}{x-4}+\frac{1}{x-2}-\frac{1}{x+1}+\frac{1}{x+1}-\frac{1}{x-5}\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(\frac{2}{x-2}-\frac{2}{x-5}\right)=0\) vì \(\frac{2}{x-2}-\frac{2}{x-5}\)luôn khác 0 nên x-1=0 nên x=1.

Điều kiện xác định : x khác 4,5,2,-1. Do đó x=1 thỏa mãn. Vậy x=1

a) \(\frac{2x-7}{10x-4}-\frac{3x+5}{4-10x}\)

\(=\frac{2x-7}{10x-4}-\frac{-\left(3x+5\right)}{-\left(4-10x\right)}\)

\(=\frac{2x-7}{10x-4}-\frac{5-3x}{10x-4}\)

\(=\frac{2x-7-\left(5-3x\right)}{10x-4}\)

\(=\frac{2x-7-5+3x}{10x-4}\)

\(=\frac{5x-12}{10x-4}\)

a: \(=\dfrac{x-2x-1}{x+1}=\dfrac{-\left(x+1\right)}{x+1}=-1\)

b: \(=\dfrac{2+2x}{x\left(x+1\right)}=\dfrac{2\left(x+1\right)}{x\left(x+1\right)}=\dfrac{2}{x}\)

c: \(=\dfrac{3x-1}{2\left(3x+1\right)}+\dfrac{3x+1}{2\left(3x-1\right)}-\dfrac{6x}{\left(3x-1\right)\left(3x+1\right)}\)

\(=\dfrac{9x^2-6x+1+9x^2+6x+1-12x}{2\left(3x-1\right)\left(3x+1\right)}=\dfrac{18x^2-12x+2}{2\left(3x-1\right)\left(3x+1\right)}\)

\(=\dfrac{2\left(3x-1\right)^2}{2\left(3x-1\right)\left(3x+1\right)}=\dfrac{3x-1}{3x+1}\)

a: \(\frac{11x-3}{3x^2-15x-42}\)

\(=\frac{11x-3}{3\left(x^2-5x-14\right)}=\frac{11x-3}{3\left(x-7\right)\left(x+2\right)}\)

\(=\frac{3\left(11x-3\right)\left(x+1\right)}{3\cdot3\cdot\left(x-7\right)\left(x+2\right)\left(x+1\right)}=\frac{3\left(11x-3\right)\left(x+1\right)}{9\left(x-7\right)\left(x+2\right)\left(x+1\right)}\)

\(\frac{8}{x^2-6x-7}=\frac{8}{x^2-7x+x-7}\)

\(=\frac{8}{\left(x-7\right)\left(x+1\right)}\)

\(=\frac{8\cdot9\cdot\left(x+2\right)}{9\left(x+2\right)\left(x-7\right)\left(x+1\right)}=\frac{72x+144}{9\left(x+2\right)\left(x-7\right)\left(x+1\right)}\)

\(\frac{13x}{9x-63}=\frac{13x}{9\left(x-7\right)}\)

\(=\frac{13x\left(x+2\right)\left(x+1\right)}{9\left(x-7\right)\left(x+2\right)\left(x+1\right)}\)

b: \(\frac{2}{x^2+2x}=\frac{2}{x\left(x+2\right)}\)

\(=\frac{2\cdot\left(x^2-2x+4\right)}{x\left(x+2\right)\left(x^2-2x+4\right)}\)

\(\frac{3x^2-6x}{x^2-2x+4}=\frac{3x\left(x-2\right)}{x^2-2x+4}=\frac{3x\left(x-2\right)\cdot x\left(x+2\right)}{x\left(x+2\right)\left(x^2-2x+4\right)}\)

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

\(\frac{10x^2+28x-8}{x^4+8x}=\frac{10x^2+28x-8}{x\left(x^3+8\right)}=\frac{10x^2+28x-8}{x\left(x+2\right)\left(x^2-2x+4\right)}\)

a) Tìm MTC:

\(\text{2x + 6 = 2(x + 3)}\)

\(\text{x2 – 9 = (x – 3)(x + 3)}\)

\(\text{MTC = 2(x – 3)(x + 3) = 2(x2 – 9)}\)

Nhân tử phụ:

\(\text{2(x – 3)(x + 3) : 2(x + 3) = x – 3}\)

\(\text{2(x – 3)(x + 3) : (x2 – 9) = 2}\)

Qui đồng:

b) Tìm MTC:

thanks bạn nha