\(\frac{6}{x^2-9}+\frac{5x}{x-3}+\frac{x}{x+3}\)

\(=\frac{6x}{\left(x-3\right)\left(x+3\right)}+\frac{5x}{x-3}+\frac{x}{x+3}\)

\(=\frac{6x}{\left(x-3\right)\left(x+3\right)}-\frac{5x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{6x+5x\left(x+3\right)+x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\)

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

\(\frac{6x}{x^2-9}+\frac{5x}{x-3}+\frac{x}{x+3}\left(x\ne\pm3\right)\)

\(=\frac{6x}{\left(x-3\right)\left(x+3\right)}+\frac{5x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{6x+5x^2+15x+x^2-3x}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{6x^2+18x}{\left(x-3\right)\left(x+3\right)}=\frac{6x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\frac{6x}{x-3}\)

\(\frac{\left(x-3\right)^3}{3x^2}:\frac{x^2-6x+9}{6x}\)

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

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

\(=\frac{2x-6}{x}\)

#H

Trả lời:

\(\frac{\left(x-3\right)^3}{3x^2}:\frac{x^2-6x+9}{6x}\)

\(=\frac{\left(x-3\right)^3}{3x^2}.\frac{6x}{x^2-6x+9}\)

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

\(=\frac{\left(x-3\right)^3.6x}{3x^2.\left(x-3\right)^2}\)

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

Cứu với mn ơi huhu !!

a: \(\dfrac{5x+y^2}{x^2y}-\dfrac{5y-x^2}{xy^2}\)

\(=\dfrac{5xy+y^3-x\left(5y-x^2\right)}{x^2y^2}\)

\(=\dfrac{5xy+y^3-5xy+x^3}{x^2y^2}=\dfrac{x^3+y^3}{x^2y^2}\)

b: \(\dfrac{x+9}{\left(x-3\right)\left(x+3\right)}-\dfrac{3}{x\left(x+3\right)}\)

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

Bài 1:

a)

 \(9x^2-49=0\)

\(9x^2-49+49=0+49.\)

\(9x^2=49\)

\(\frac{9x^2}{9}=\frac{49}{9}\)

\(x^2=\frac{49}{9}\)

\(x=\sqrt{\frac{49}{9}}\)

\(x=\frac{\sqrt{49}}{\sqrt{9}}\)

\(x=\frac{7}{3}\)hay \(x=2,33333...\)

b)

\(\left(x-1\right)\left(x+2\right)-x-2=0.\)

\(x^2+x-2-x-2.\)

\(x^2+\left(x-x\right)-\left(2+2\right)=\)\(0\)

\(x^2-4=0\)

\(x=\sqrt{4}\)

\(x=2\)

Bài 2:

a)

      \(\frac{x}{x}-3+9-\frac{6x}{x^2}-3x.\)

\(=1-3+9-\frac{6x}{x^2}-3x.\)

\(=1-3+9-\frac{6}{x}-3x.\)

\(=7-\frac{6}{x}-3x\)

b)

       \(6x-\frac{3}{x}\div4x^2-\frac{1}{3x^2}\)

\(=6x-\frac{3}{x}\div\frac{4}{1}x^2-\frac{1}{3x^2}.\)

\(=6x-\frac{3}{x}\times\frac{1}{4}x^2-\frac{1}{3x^2}\)

\(=6x-\frac{3x^2}{x4}-\frac{1}{3x^2}\)

\(=6x-\frac{3x}{4}-\frac{1}{3x^2}\)

\(=\frac{6x}{1}-\frac{3x}{4}-\frac{1}{3x^2}\)

\(=\frac{72x^3-36x^3-12x^2}{12x^2}\)

\(=\frac{36-12x^2}{12x^2}\)

a,       x² - 9 - x² - 3x + 10 = 1 - 3x

\(\frac{x^2+3x+9}{2x+10}.\frac{x+5}{x^3-27}\)

\(=\frac{x^2+3x+9}{2\left(x+5\right)}.\frac{x+5}{\left(x-3\right)\left(x^2+3x+9\right)}\)

\(=\frac{\left(x+5\right)\left(x^2+3x+9\right)}{2\left(x+5\right)\left(x-3\right)\left(x^2+3x+9\right)}\)

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

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

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

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

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

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

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

\(=\frac{12}{x}\)

1)(x+1)(x+2)(x+3)=x³+6x²+11x+6

2)a)3x(x-5)-(x-1)(2+3x)=30

<=>3x²-15x-3x²+x+2=30

<=>-14x+2=30

<=>-14x=30-2

<=>-14x=28

<=>x=-2

b)(x+2)(x+3)-(x-2)(x+5)=0

<=>x²+5x+6-x²-3x+10=0

<=>2x+16=0

<=>2x=-16

<=>x=-8

c)(3x+2)(2x+9)-(x+2)(6x+1)=9

<=>6x²+31x+18-6x²-13x-2=9

<=>18x+16=9

<=>18x=9-16

<=>18x=-7

<=>x=-7/18