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

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

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

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

a) Ta có: \(\frac{x^2+3x+2}{3x+6}\) \(\left(x\ne-2\right)\)

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

\(=\frac{x+1}{3}\)

b) Ta có: \(\frac{2x^2+x-1}{6x-3}\) \(\left(x\ne\frac{1}{2}\right)\)

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

\(=\frac{x+1}{3}\)

\(a,\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\) (x khác -3; khác 0)

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

\(b,\left(\frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}\right):\frac{4x}{10x-5}\) (x khác 0 , khác 1/2 khác -1/2 )

\(=\left(\frac{\left(2x+1\right)^2}{\left(2x-1\right)\left(2x+1\right)}-\frac{\left(2x-1\right)^2}{\left(2x-1\right)\left(2x+1\right)}\right).\frac{10x-5}{4x}\)

\(=\left(\frac{4x^2+4x+1}{\left(2x-1\right)\left(2x+1\right)}-\frac{4x^2-4x+1}{\left(2x-1\right)\left(2x+1\right)}\right).\frac{10x-5}{4x}\)

\(=\frac{8x}{\left(2x-1\right)\left(2x+1\right)}.\frac{5.\left(2x-1\right)}{4x}=\frac{10}{2x+1}\)

\(c,\frac{x^2+x}{5x^2-10x+5}:\frac{3x+3}{5x-5}\) (x khác 1 ; khác -1)

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

a) \(\frac{x^2+2x-3}{x^2+x-6}\)

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

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

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

\(=\frac{x-1}{x-2}\)

b) \(\frac{2x^2+2x+2}{x^2+6x-7}\)

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

\(cogidosaisai?\)

= ( x/(x-6)(x+6) - x-6/x(x+6) ) : 2x-6/x² + 6x + 6/6-x

=(  x²/x(x+6)(x-6) - (x -6 )(x-6)/x(x+6)(x-6)  ) : .....

= (12x -36 / x(x+6)(x-6) : 2x-6/ x² + 6x )+ 6/6-x

=6/x-6 + 6/6-x

= 6-6/ x-6

=0/x-6 

câu trước mình thiếu 6/6-x

bạn ơi kết quả bằng 6/x-6

câu trên sai , để mình giải đàng hoàng ra 

1. Cho bt P= (1/√x+2 + 1/√x-2 ) . √x-2/√x với x>0, x khác 4

a) rút gọn P

b) tìm x để P>1/3

c) tìm các giá trị thực của x để Q=9/2P có giá trị nguyên

2. Cho 2 biểu thức

A= 1-√x / 1+√ x và B= ( 15-√x/ x-25 + 2/√x+5) : √x+1/√ x-5 với x lớn hơn hoặc bằng 0, x khác 25

a) tính giá trị của A khi x= 6-2√5

b) rút gọn B

c) tìm a để pt A-B=a có nghiệm

chúc bạn học tốt

Bài 1 :

\(a,P=\left(\frac{x}{x^2-36}-\frac{x-6}{x^2+6x}\right):\frac{2x-6}{x^2+6x}=\left[\frac{x}{\left(x+6\right)\left(x-6\right)}-\frac{x-6}{x\left(x+6\right)}\right]:\frac{2x-6}{x\left(x+6\right)}\)

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

\(=\frac{6}{x-6}\)

\(b,\)Với \(x\ne-6;x\ne6;x\ne0;x\ne3\)  Thì

\(P=1\Rightarrow\frac{6}{X-6}=1\Rightarrow6=x-6\Rightarrow x=12\)(Thỏa mãn \(ĐKXĐ\))

\(c,\)Ta có :

\(P< 0\Rightarrow\frac{6}{X-6}< 0\Rightarrow X-6< 0\Rightarrow X< 6\)

Do :  \(x\ne-6;x\ne6;x\ne0;x\ne3\)  ,Nên với \(x< 6\)và  \(x\ne-6;x\ne0;x\ne3\)  thì \(P< 0\)

Bài 1 : 

a ) Ta có : 

\(P=\left(\frac{x}{x^2-36}-\frac{x-6}{x^2+6x}\right):\frac{2x-6}{x^2+6x}\)

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

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

\(=\frac{x^2-x^2+12x-36}{x-6}.\frac{1}{2\left(x-3\right)}\)

\(=\frac{12\left(x-3\right)}{x-6}.\frac{1}{2\left(x-3\right)}\)

\(=\frac{6}{x-6}\)

b ) \(P=1\Leftrightarrow\frac{6}{x-6}=1\Leftrightarrow x-6=6\Leftrightarrow x=12\left(tm\right)\)

c ) \(p< 0\Leftrightarrow\frac{6}{x-6}< 0\Leftrightarrow x-6< 0\Rightarrow x< 6\)