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$\dfrac{5x+10}{4x-8}\cdot\dfrac{4-2x}{x+2}$
$=\dfrac{5(x+2)}{4(x-2)}\cdot\dfrac{-2(x-2)}{x+2}$
$=-\dfrac{10}{4}$
$=-\dfrac{5}{2}$
$\dfrac{6x^2y^3}{8x^3y^2}$
$=\dfrac{3y}{4x}$
b)$\dfrac{x^3-x}{3x+3}$
$=\dfrac{x(x^2-1)}{3(x+1)}$
$=\dfrac{x(x-1)(x+1)}{3(x+1)}$
$=\dfrac{x(x-1)}{3}$
c)$\dfrac{x^2+3xy}{x^2-9y^2}$
$=\dfrac{x(x+3y)}{(x-3y)(x+3y)}$
$=\dfrac{x}{x-3y}$
d)$\dfrac{x^2+4x+4}{3x+6}$
$=\dfrac{(x+2)^2}{3(x+2)}$
$=\dfrac{x+2}{3}$
a) ( 3x - 2 )( 4x + 5 ) - 6x( 2x - 1 )
= 12x2 + 7x - 10 - 12x2 + 6x
= 13x - 10
b) ( 2x - 5 )2 - 4( x + 3 )( x - 3 )
= 4x2 - 20x + 25 - 4( x2 - 9 )
= 4x2 - 20x + 25 - 4x2 + 36
= 61 - 20x
c) 2x3 - 5x2 + 7x - 6
= 2x3 - 3x2 - 2x2 + 3x + 4x - 6
= x2( 2x - 3 ) - x( 2x - 3 ) + 2( 2x - 3 )
= ( 2x - 3 )( x2 - x + 2 )
=> ( 2x3 - 5x2 + 7x - 6 ) : ( 2x - 3 ) = x2 - x + 2
a, (3x - 2 ) (4x + 5) - 6x (2x -1) = ( 7x + 15x -8x - 10 ) - ( 12x2 -6x ) = 7x2 + 15x - 8x -10 -12x2 + 6x = -5x2 + x - 10
a: \(=\dfrac{4x-8+2x+4-8}{\left(x-2\right)\left(x+2\right)}=\dfrac{6x-12}{\left(x-2\right)\left(x+2\right)}=\dfrac{6}{x+2}\)
b: \(=\dfrac{-x+7x-4}{3x-2}=\dfrac{6x-4}{3x-2}=2\)
c: \(=\dfrac{x}{2x+1}-\dfrac{1}{\left(2x+1\right)\left(2x-1\right)}-\dfrac{\left(x-2\right)}{2x-1}\)
\(=\dfrac{2x^2-x-1-\left(x-2\right)\left(2x+1\right)}{\left(2x+1\right)\left(2x-1\right)}\)
\(=\dfrac{2x^2-x-1-2x^2-x+4x+2}{\left(2x+1\right)\left(2x-1\right)}\)
\(=\dfrac{2x+1}{\left(2x+1\right)\left(2x-1\right)}=\dfrac{1}{2x-1}\)
d: \(=\dfrac{5}{2x-3}+\dfrac{2}{2x+3}+\dfrac{2x-33}{4x^2-99}\)
\(=\dfrac{10x+15+4x-6+2x-33}{\left(2x-3\right)\left(2x+3\right)}=\dfrac{16x-24}{\left(2x-3\right)\left(2x+3\right)}=\dfrac{8}{2x+3}\)
\(a,=12x^2-4x-6x-2-x-3=12x^2-11x-5\\ b,=12x^2-9x-12x^2-4x+5=5-13x\\ c,=12x^3-4x^2-12x^3-12x^2+7x-3=-16x^2+7x-3\\ d,=\left(x^2-4\right)\left(x^2+4\right)=x^4-16\)
a)xy(x2+2y)=xy.x2+xy.2y
=x3y+2xy2
b)-4(6x2-xy)=-4.6x2+4.xy
=-24x2+4xy
c)4x[x2+6x-1/2]
=4x.x2+4x.6x-4x.1/2
=4x3+24x2-2x
a,\(2x\left(x^2-3x+4\right)\)
\(=2x^3-6x+8x\)
b,\(\left(x+2\right)\left(x-1\right)\)
\(=x^2-x+2x-2\)
\(=x^2+x-2\)
c,\(\left(4x^4-2x^3+6x^2\right):2x\)
\(=2x^3-x^2+3x\)
a.2x( x\(^2\) - 3x +4 )
= 2x\(^3\) - 6x\(^2\) + 8x
b. ( x + 2 )( x - 1 )
= x\(^2\) - x + 2x - 2
= x\(^2\) + x - 2
c. ( 4x\(^4\) - 2x\(^3\) + 6x\(^2\) ) : 2x
= 2x\(^3\) - x\(^2\) + 3x