Bài 1: Thực hiện phép tính
a, (5x-2y)(x\(^2\)-xy+1)
b, (x-1)(x+1)(x+2)
c, \(\dfrac{1}{2}\)x\(^2\)y\(^2\)(2x+y)(2x-y)
d, (x-\(\dfrac{1}{2}\))(x+\(\dfrac{1}{2}\))(4x-1)
e, (x-7)(x+5)-(2x+1)(3-x)
Thực hiện phép tính:
a) \(\dfrac{x+2y}{xy}\div\dfrac{x^2+4xy+4y^2}{2x^2}\)
b) \(\dfrac{4x^3-xy^2}{x^2+xy+y^2}\div\dfrac{\left(2x-y\right)^3}{x^3-y^3}\)
c) \(\dfrac{x+3}{x+2}\div\dfrac{3x+9}{2x-1}\div\dfrac{4x-2}{2x+4}\)
d) \(\dfrac{x+1}{x+2}\div\left(\dfrac{2x^2}{2x-3}\times\dfrac{3x+3}{4x^3}\right)\)
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: \(=\dfrac{x+1}{x+2}:\left(\dfrac{1}{2x}\cdot\dfrac{3x+3}{2x-3}\right)\)
\(=\dfrac{x+1}{x+2}\cdot\dfrac{2x\left(2x-3\right)}{3\left(x+1\right)}=\dfrac{2x\left(2x-3\right)}{3\left(x+2\right)}\)
thực hiện phép tính:
a) \(\dfrac{1}{2}\)x\(^3\) . (x\(^2\)-6\(^x\)-10)
b) -3x\(^2\) . ( 5x\(^3\)-4x\(^2\)+3x-1)
c) 3x . ( 5x\(^2\) - 2x - 1)
d) \(\dfrac{1}{2}\)x\(^2\)y . ( 2x\(^3\)-\(\dfrac{2}{5}\)xy\(^2\)-1)
a: =1/2x^3*x^2-1/2x^3*6x-1/2x^3*10
=1/2x^5-3x^4-5x^3
b: =-3x^2*5x^3+3x^2*4x^2-3x^2*3x+3x^2*3x
=-15x^5+12x^4-9x^3+9x^2
c: \(=3x\cdot5x^2-3x\cdot2x-3x=15x^3-6x^2-3x\)
d: \(=\dfrac{1}{2}x^2y\cdot2x^3-\dfrac{1}{2}x^2y\cdot\dfrac{2}{5}xy^2-\dfrac{1}{2}x^2y=x^5y-\dfrac{1}{5}x^3y^3-\dfrac{1}{2}x^2y\)
BT10: Thực hiện phép tính
\(a,\dfrac{4}{5}y^2x^5-x^3.x^2y^2\)
\(b,-xy^3-\dfrac{2}{7}y^2.xy\)
\(c,\dfrac{5}{6}xy^2z-\dfrac{1}{4}xyz.y\)
\(d,15x^4+7x^4-20x^2.x^2\)
\(e,\dfrac{1}{2}x^5y-\dfrac{3}{4}x^5y+xy.x^4\)
\(f,13x^2y^5-2x^2y^5+x^6\)
a: =-1/5x^5y^2
b: =-9/7xy^3
c: =7/12xy^2z
d: =2x^4
e: =3/4x^5y
f: =11x^2y^5+x^6
Thực hiện phép tính:
a) \(\dfrac{x}{2x-y}-\dfrac{2x-y}{4x-2y}\)
b)\(\dfrac{3x+1}{x^2-1}-\dfrac{x}{2x-2}\)
c) \(\dfrac{x-2}{x^2-4}-\dfrac{-8-x}{3x^2+6x}\)
d) \(\dfrac{2}{2x-3}-\dfrac{x}{2x+3}-\dfrac{2x+1}{9-4x^2}\)
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: \(=\dfrac{4x+6-2x^2+3x+2x+1}{\left(2x-3\right)\left(2x+3\right)}\)
\(=\dfrac{-2x^2+9x+7}{\left(2x-3\right)\left(2x+3\right)}\)
A = \(\dfrac{5xy^2-3z}{3xy}+\dfrac{4x^2y+3z}{3xy}\)
B = \(\dfrac{3y+5}{y-1}+\dfrac{-y^2-4y}{1-y}+\dfrac{y^2+y+7}{y-1}\)
C = \(\dfrac{6x}{x^2-9}+\dfrac{5x}{x-3}+\dfrac{x}{x+3}\)
D = \(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{3x-2}{2x-4x^2}\)
E = \(\dfrac{x^3+2x}{x^3+1}+\dfrac{2x}{x^2-x+1}+\dfrac{1}{x+1}\)
b: \(B=\dfrac{3y+5}{y-1}-\dfrac{-y^2-4y}{y-1}+\dfrac{y^2+y+7}{y-1}\)
\(=\dfrac{3y+5+y^2+4y+y^2+y+7}{y-1}\)
\(=\dfrac{2y^2+8y+12}{y-1}\)
Thực hiện phép tính
a) \(\dfrac{3-x}{x-5}+\dfrac{2x-8}{x-5}\)
b) \(\dfrac{1}{x-y}+\dfrac{1}{x+y}+\dfrac{2x}{x^2-y^2}\)
a,\(\dfrac{3-x}{x-5}+\dfrac{2x-8}{x-5}=\dfrac{3-x+2x-8}{x-5}=\dfrac{x-5}{x-5}=1\)
b, \(\dfrac{1}{x-y}+\dfrac{1}{x+y}+\dfrac{2x}{x^2-y^2}=\dfrac{x+y}{\left(x-y\right)\left(x+y\right)}+\dfrac{x-y}{\left(x-y\right)\left(x+y\right)}+\dfrac{2x}{\left(x-y\right)\left(x+y\right)}=\dfrac{x+y+x-y+2x}{\left(x-y\right)\left(x+y\right)}=\dfrac{4x}{\left(x-y\right)\left(x+y\right)}\)
1, Thực hiện phép tính:
a, \(\dfrac{1-3x}{2}+\dfrac{x+3}{2}\)
b, \(\dfrac{2\left(x+y\right)\left(x-y\right)}{x}-\dfrac{-2y^2}{x}\)
c, \(\dfrac{3x+1}{x+y}-\dfrac{2x-3}{x+y}\)
d, \(\dfrac{xy}{2x-y}-\dfrac{x^2-1}{y-2x}\)
e, \(\dfrac{4x-1}{3x^2y}-\dfrac{7x-1}{3x^2y}\)
2, Thực hiện phép tính:
a, \(\dfrac{1}{x}.\dfrac{6x}{y}\)
b, \(\dfrac{2x^2}{y}.3xy^2\)
c, \(\dfrac{15x}{7y^3}.\dfrac{2y^2}{x^2}\)
d, \(\dfrac{2x^2}{x-y}.\dfrac{y}{5x^3}\)
e, \(\dfrac{5x+10}{4x-8}.\dfrac{4-2x}{x+2}\)
f, \(\dfrac{x^2-36}{2x+10}.\dfrac{3}{6-x}\)
2)
a) \(\dfrac{1}{x}.\dfrac{6x}{y}\)
\(=\dfrac{6x}{xy}\)
\(=\dfrac{6}{y}\)
b) \(\dfrac{2x^2}{y}.3xy^2\)
\(=\dfrac{2x^2.3xy^2}{y}\)
\(=\dfrac{6x^3y^2}{y}\)
\(=6x^3y\)
c) \(\dfrac{15x}{7y^3}.\dfrac{2y^2}{x^2}\)
\(=\dfrac{15x.2y^2}{7y^3.x^2}\)
\(=\dfrac{30xy^2}{7x^2y^3}\)
\(=\dfrac{30}{7xy}\)
d) \(\dfrac{2x^2}{x-y}.\dfrac{y}{5x^3}\)
\(=\dfrac{2x^2.y}{\left(x-y\right).5x^3}\)
\(=\dfrac{2y}{5x\left(x-y\right)}\)
Thực hiện các phép tính sau:
a).\(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\)
b). \(\left(\dfrac{1}{x^2+1}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
c). \(\dfrac{1}{x-1}-\dfrac{x^3-x}{x^2+1}.\left(\dfrac{1}{x^2-2x+1}+\dfrac{1}{1-x^2}\right)\)
d). \(\left(\dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+\dfrac{y}{x^2+y^2}\right):\left(\dfrac{1}{x-y}-\dfrac{2xy}{x^3-x^2y+xy^2-y^3}\right)\)
a) \(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\)
\(=\left(\dfrac{\left(2x+1\right)\left(2x+1\right)}{2x^2-1}-\dfrac{\left(2x-1\right)\left(2x-1\right)}{2x^2-1}\right):\dfrac{4x}{10x-5}\)
\(=\left(\dfrac{\left(2x+1\right)^2-\left(2x-1\right)^2}{2x^2-1}\right):\dfrac{4x}{10x-5}\)
\(=\left(\dfrac{\left(2x+1-2x-1\right)\left(2x+1+2x-1\right)}{2x^2-1}\right):\dfrac{4x}{10x-5}\)
\(=\dfrac{4x}{2x^2-1}.\dfrac{5\left(2x-1\right)}{4x}\)
\(=\dfrac{5}{2x+1}\)
b) \(\left(\dfrac{1}{x^2+1}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(=\left(\dfrac{1}{x^2+1}-\dfrac{x\left(2-x\right)}{x\left(x+1\right)}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(=\left(\dfrac{1-2x+x^2}{x^2+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(=\left(\dfrac{1-2x+x^2}{x^2+1}\right):\left(\dfrac{1}{x}+\dfrac{x^2}{x}-\dfrac{2x}{x}\right)\)
\(=\left(\dfrac{1-2x+x^2}{x^2+1}\right):\left(\dfrac{x^2-2x+1}{x}\right)\)
\(=\dfrac{\left(x-1\right)^2}{x^2+1}.\dfrac{x}{\left(x-1\right)^2}\)
\(=\dfrac{x}{x^2+1}\)
c) d) Tự làm đi mình làm biếng quass >.< ^^