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3 tháng 9 2021

a) \(\left(6x^2y-\dfrac{1}{2}xy+12y\right)\left(-\dfrac{1}{3}xy\right)=-2x^3y^2+\dfrac{1}{6}x^2y^2-4xy^2\)

b) \(\left(2x+3-y\right)\left(2x-y\right)=4x^2+6x-2xy-2xy-3y+y^2=4x^2+y^2+6x-3y-4xy\)

c) \(3\left(4x+1\right)\left(4x-1\right)-12\left(4x^2+1\right)=3\left(16x^2-1\right)-48x^2-12=48x^2-3-48x^2-12=-15\)

3 tháng 9 2021

b. (2x + 3 - y)(2x - y)

= 4x2 - 2xy + 6x - 3y - 2xy + y2

= 4x2 - 4xy + 6x - 3y + y2

\(\left[\left(2x\right)^2-4xy+y^2\right]\) + (6x - 3y)

= (2x - y)2 + 3(2x - y)

= (2x - y + 3)(2x - y)

a: \(=\dfrac{x+2y}{xy}\cdot\dfrac{2x^2}{\left(x+2y\right)^2}=\dfrac{2x}{y\left(x+2y\right)}\)

b: \(=\dfrac{x\left(4x^2-y^2\right)}{x^2+xy+y^2}\cdot\dfrac{\left(x-y\right)\left(x^2+xy+y^2\right)}{\left(2x-y\right)^3}\)

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

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

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

=1/3

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

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

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

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

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

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

c: \(=\dfrac{1}{x+2}+\dfrac{x+8}{3x\left(x+2\right)}\)

\(=\dfrac{3x+x+8}{3x\left(x+2\right)}=\dfrac{4x+8}{3x\left(x+2\right)}=\dfrac{4}{3x}\)

d: \(=\dfrac{4x+6-2x^2+3x+2x+1}{\left(2x-3\right)\left(2x+3\right)}\)

\(=\dfrac{-2x^2+9x+7}{\left(2x-3\right)\left(2x+3\right)}\)

12 tháng 9 2021

2.

a. 3x(12x - 4) - 9x(4x - 3) = 30

<=> 36x2 - 12x - 36x2 + 27x = 30

<=> 36x2 - 36x2 - 12x + 27x = 30

<=> 15x = 30

<=> x = 2

b. x(5 - 2x) + 2x(x - 1) = 15

<=> 5x - 2x2 + 2x2 - 2x = 15

<=> -2x2 + 2x2 + 5x - 2x = 15

<=> 3x = 15

<=> x = 5

12 tháng 9 2021

a) x2 ( 5x3 - x - 1212)= 5x5-x3-1212x

b) ( 3xy - x2 + y ) 2323x2y=  6969x3y2- 2323x4y+ 2323x2y2

c) x2 ( 4x3 - 5xy + 2x ) ( -1212 xy )=(4x5-5x3y+2x3).(-1212xy)

                                                      = -4848x6y +6060x4y2-2424x4y

2/ Tìm x, biết

a) 3x( 12x - 4 ) - 9x (4x - 3 ) = 30

=> 36x2-12x-36x2+27x=30

=> -12x +27x=30

=> 15x = 30

=>x =2

 

b ) x( 5 - 2x ) + 2x ( x - 1 )= 15

=> 5x-2x2+2x2-2x=15

=> 3x=15

=>x=5

3 tháng 12 2021

Giúp với mọi người

 

 

c: \(=3x^3-4x^2+6x^2-8x=3x^2+2x^2-8x\)

23 tháng 11 2017

a) \(\dfrac{2x+y}{2x^2-xy}+\dfrac{8y}{y^2-4x^2}+\dfrac{2x-y}{2x^2+xy}\)

\(=\dfrac{2x+y}{x\left(2x-y\right)}+\dfrac{-8y}{y^2-4x^2}+\dfrac{2x-y}{2x^2+xy}\)

\(=\dfrac{\left(2x+y\right)\left(2x+y\right)-8yx+\left(2x-y\right)\left(2x-y\right)}{x\left(2x+y\right)\left(2x-y\right)}\)

\(=\dfrac{8x^2-8xy+2y^2}{x\left(2x+y\right)\left(2x-y\right)}\)

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

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

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

b) \(\dfrac{1}{x^2+3x+2}+\dfrac{2x}{x^2+4x+3}+\dfrac{1}{x^2+5x+6}\)

\(=\dfrac{1}{x^2+x+2x+2}+\dfrac{2x}{x^2+x+3x+3}+\dfrac{1}{x^2+2x+3x+6}\)

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

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

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

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

\(=\dfrac{2x^2+6x+4}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}\)

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

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

\(=\dfrac{2}{x+3}\)

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

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

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

d: \(=\dfrac{x^3-1}{x-1}-\dfrac{x^2-1}{x+1}\)

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