cho mình hỏi là giữa khác phân số với nhua là phải có dấu như là công, trừ, nhân hay chia chứ? 

MTC : ( x - 1 )( x² + x + 1 )

Ta có : \(\frac{4x^2-3x+5}{x^3-1}=\frac{4x^2-3x+5}{\left(x-1\right)\left(x^2+x+1\right)}\)

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

\(\frac{6}{x-1}=\frac{6\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=\frac{6x^2+6x+6}{\left(x-1\right)\left(x^2+x+1\right)}\)

Hnay mới học thì hnay trả lời nhá :P

\(\frac{4x^2-3x+5}{x^3-1};\frac{2x}{x^2+x+1}\)

Ta có : \(x^3-1=\left(x-1\right)\left(x^2+x+1\right)\)

\(x^2+x+1=x^2+x+1\)

MTC : \(\left(x-1\right)\left(x^2+x+1\right)\)

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

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

\(\frac{2x}{x^2+x+1};\frac{6}{x-1}\)

Ta có : \(x^2+x+1=x^2+x+1\)

\(x-1=x-1\)

MTC : \(\left(x^2+x+1\right)\left(x-1\right)=x^3-1\)

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

\(\frac{6}{x-1}=\frac{6\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=\frac{6x^2+6x+6}{x^3-1}\)

a) Tìm MTC: x3 – 1 = (x – 1)(x2 + x + 1)

Nên MTC = (x – 1)(x2 + x + 1)

Nhân tử phụ:

(x3 – 1) : (x3 – 1) = 1

(x – 1)(x2 + x + 1) : (x2 + x + 1) = x – 1

(x – 1)(x2+ x + 1) : 1 = (x – 1)(x2 + x + 1)

Qui đồng:

b) Tìm MTC: x + 2

2x – 4 = 2(x – 2)

6 – 3x = 3(2 – x)

MTC = 6(x – 2)(x + 2)

Nhân tử phụ:

6(x – 2)(x + 2) : (x + 2) = 6(x – 2)

6(x – 2)(x + 2) : 2(x – 2) = 3(x + 2)

6(x – 2)(x + 2) : -3(x – 2) = -2(x + 2)

Qui đồng:

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

\(\dfrac{2x-3}{2x^2-18}=\dfrac{2x-3}{2\left(x-3\right)\left(x+3\right)}=\dfrac{\left(2x-3\right)\cdot\left(2x-3\right)}{2\left(2x-3\right)\left(x-3\right)\left(x+3\right)}\)

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

\(\dfrac{2}{2x^2+3x-9}=\dfrac{2}{\left(x+3\right)\left(2x-3\right)}=\dfrac{2\cdot2\cdot\left(x-3\right)}{2\left(x-3\right)\cdot\left(x+3\right)\left(2x-3\right)}\)

\(=\dfrac{4x-12}{2\left(x-3\right)\left(x+3\right)\left(2x-3\right)}\)

a) \(\dfrac{1}{x^3-8}=\dfrac{1}{\left(x-2\right)\left(x^2+2x+4\right)}=\dfrac{2}{2\left(x-2\right)\left(x^2+2x+4\right)}\)

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

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

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

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

\(\dfrac{1}{x^2-4x+4}=\dfrac{1}{\left(x-2\right)^2}=\dfrac{x+2}{\left(x+2\right)\left(x-2\right)^2}\)

\(\dfrac{5}{2-x}=\dfrac{-5}{x-2}=\dfrac{-5\left(x+2\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)^2}\)

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

\(\dfrac{2x}{x^2-y^2}=\dfrac{2x}{\left(x+y\right)\left(x-y\right)}=\dfrac{6x\left(x-y\right)}{3\left(x+y\right)\left(x-y\right)^2}\)

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

Lời giải:
$\frac{4x^2-3x+8}{x^3-1}$
$\frac{2x}{x^2+x+1}=\frac{2x(x-1)}{(x-1)(x^2+x+1)}=\frac{2x^2-2x}{x^3-1}$

$\frac{6}{1-x}=\frac{-6(x^2+x+1)}{(x-1)(x^2+x+1)}=\frac{-6x^2-6x-6}{x^3-1}$

\(\dfrac{3}{5}x-\dfrac{1}{2}x=\dfrac{3}{2}-0\)

\(\left(\dfrac{3}{5}-\dfrac{1}{2}\right)x=\dfrac{3}{2}\)

\(\dfrac{1}{10}\cdot x=\dfrac{3}{2}\)

\(x=\dfrac{3}{2}:\dfrac{1}{10}\)

\(x=15\)

\(\dfrac{3}{5x}-\dfrac{1}{2x}=\dfrac{3}{2-0}\)

\(\dfrac{3}{5x}+\dfrac{-1}{2x}=\dfrac{3}{2}\)

\(\dfrac{3}{5}+\dfrac{-1}{2}=\dfrac{3}{2}\cdot x\)

\(\dfrac{1}{10}=\dfrac{3}{2}\cdot x\)

\(\dfrac{3}{2}\cdot x=\dfrac{1}{10}\)

     \(x=\dfrac{1}{10}\div\dfrac{3}{2}\)

    \(x=\dfrac{2}{30}\)

    \(x=\dfrac{1}{15}\)