Thực hiện phép tính:
2y : \(\dfrac{4x}{5xy}\). \(\dfrac{64xy}{100x^3y^4}\)
thực hiện phép tính
(x^2-y^2).\(\dfrac{x^2+y^2}{y^4-x^2y^2}\)
\(\dfrac{4x^2-9y^2}{xy}\):(2x-3y)
Ta có:(x2-y2)\(.\dfrac{x^2+y^2}{y^4-x^2y^2}\)\(=\left(x^2-y^2\right).\dfrac{x^2+y^2}{y^2\left(y^2-x^2\right)}=-\dfrac{x^2+y^2}{y^2}\)
Ta có:\(\dfrac{4x^2-9y^2}{xy}:\left(2x-3y\right)=\dfrac{\left(2x-3y\right)\left(2x+3y\right)}{xy}.\dfrac{1}{\left(2x-3y\right)}=\dfrac{2x+3y}{xy}\)
Thực hiện phép tính :
a/ (x - 1)^2 - (4x + 3) (2 - x)
b/ (15x^3y^2 - 6x^2y^3) : 3x^2y^2 = (15x^3y^2 : 3x^2y^2) - (6x^2y^3 : 3x^2y^2) = 5x - 2y
c/\(\dfrac{x+7}{x-7}\) - \(\dfrac{x-7}{x+7}\) +\(\dfrac{4x^2}{x^2-49}\)
a/ (x-1)2-(4x+3)(2-x)=x2-2x+1-(8x-4x2+6-3x)
=x2-2x+1-8x+4x2-6+3x=5x2-7x-6
b/ (15x3y2 - 6x2y3) : 3x2y2 = 5x - 2y
c/ \(\dfrac{x+7}{x-7}-\dfrac{x-7}{x+7}+\dfrac{4x^2}{x^2-49}\)=\(\dfrac{\left(x+7\right)^2-\left(x-7\right)^2+4x^2}{\left(x-7\right)\left(x+7\right)}\)=\(\dfrac{x^2+14x+49-\left(x^2-14x+49\right)+4x^2}{\left(x-7\right)\left(x+7\right)}\)=\(\dfrac{28x+4x^2}{\left(x-7\right)\left(x+7\right)}\)=\(\dfrac{4x\left(x+7\right)}{\left(x-7\right)\left(x+7\right)}\)=\(\dfrac{4x}{x-7}\)
\(\dfrac{6\left(4-4x+x^2\right)}{x^3y}:\dfrac{x-2}{x^3y^2}\)
Thực hiện phép tính
\(=\dfrac{6\left(x-2\right)^2}{x^3y}\cdot\dfrac{x^3y^2}{x-2}=6\left(x-2\right)\cdot y\)
Thực hiện các phép tính sau :
a) \(\dfrac{3x-5}{7}+\dfrac{4x+5}{7}\)
b) \(\dfrac{5xy-4y}{2x^2y^3}+\dfrac{3xy+4y}{2x^2y^3}\)
c) \(\dfrac{x+1}{x-5}+\dfrac{x-18}{x-5}+\dfrac{x+2}{x-5}\)
Thực hiện phép tính
\(a,\dfrac{2}{x^2y}\)\(-\dfrac{4xy^2-1}{2x^3y^3}\)
Lời giải:
\(\frac{2}{x^2y}-\frac{4xy^2-1}{2x^3y^3}=\frac{4xy^2}{2x^3y^3}-\frac{4xy^2-1}{2x^3y^3}=\frac{4xy^2-(4xy^2-1)}{2x^3y^3}=\frac{1}{2x^3y^3}\)
a,\(\dfrac{x+1}{x-3}+\dfrac{-2x^2+2x}{x^2-9}+\dfrac{x-1}{x+3}\)
b,\(\dfrac{1-2x}{6x^3y}+\dfrac{3+2y}{6x^3y}+\dfrac{2x-4}{6x^3y}\)
c,\(\dfrac{5}{2x^2y}+\dfrac{3}{5xy^2}+\dfrac{x}{3y^3}\)
d,\(\dfrac{5}{4\left(x+2\right)}+\dfrac{8-x}{4x^2+8x}\)
c,\(\dfrac{x^2+2}{x^3+1}+\dfrac{2}{x^2+x+1}+\dfrac{1}{1-x}\)
\(a,=\dfrac{x^2+4x+3-2x^2+2x+x^2-4x+3}{\left(x-3\right)\left(x+3\right)}=\dfrac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{2}{x-3}\\ b,=\dfrac{1-2x+3+2y+2x-4}{6x^3y}=\dfrac{2y}{6x^3y}=\dfrac{1}{x^2}\\ c,=\dfrac{75y^2+18xy+10x^2}{30x^2y^3}\\ d,=\dfrac{5x+8-x}{4x\left(x+2\right)}=\dfrac{4\left(x+2\right)}{4x\left(x+2\right)}=\dfrac{1}{x}\\ c,=\dfrac{x^2+2+2x-2-x^2-x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{1}{x^2+x+1}\)
Bài 1: Thực hiện phép tính
a) (x-4) (x+4) - (5-x) (x+1)
b) (3x^2 - 2xy + 4) + ( 5xy - 6x^2 - 7)
Bài 2: Rút gọn biểu thức
a) 3x^2 (2x + y) - 2y(4x^2 - y)
b) (x+3y) (x-2y) - (x^4 - 6x^2y^3): x^2y
Bài 1:
a, (\(x\) - 4).(\(x\) + 4) - (5 - \(x\)).(\(x\) + 1)
= \(x^2\) - 16 - 5\(x\) - 5 + \(x^2\) + \(x\)
= (\(x^2\) + \(x^2\)) - (5\(x\) - \(x\)) - (16 + 5)
= 2\(x^2\) - 4\(x\) - 21
b, (3\(x^2\) - 2\(xy\) + 4) + (5\(xy\) - 6\(x^2\) - 7)
= 3\(x^2\) - 2\(xy\) + 4 + 5\(xy\) - 6\(x^2\) - 7
= (3\(x^2\) - 6\(x^2\)) + (5\(xy\) - 2\(xy\)) - (7 - 4)
= - 3\(x^2\) + 3\(xy\) - 3
Bài 2:
a, 3\(x^2\).(2\(x\) + y) - 2y(4\(x^2\) - y)
= 6\(x^3\) + 3\(x^2\).y - 8y\(x^2\) + 2y2
= 6\(x^3\) - (8\(x^2\)y - 3\(x^2\)y) + 2y2
= 6\(x^3\) - 5\(x^2\)y + 2y2
Bài 3:
3: \(6x\left(x-y\right)-9y^2+9xy\)
\(=6x\left(x-y\right)+9xy-9y^2\)
\(=6x\left(x-y\right)+9y\left(x-y\right)\)
\(=\left(x-y\right)\left(6x+9y\right)\)
\(=3\left(2x+3y\right)\left(x-y\right)\)
Bài 4:
BT10: Thực hiện phép tính
\(a,-xyz^2\)\(-3xz.yz\)
\(b,-8x^2\)\(y-x.\left(xy\right)\)
\(c,4xy^2\) \(.x-\left(-12x^2y^2\right)\)
\(d,\dfrac{1}{2}x^2y^3-\dfrac{1}{3}x^2y.y^2\)
\(e,3xy\left(x^2y\right)-\dfrac{5}{6}x^3y^2\)
\(f,\dfrac{3}{4}x^4y-\dfrac{1}{6}xy.x^3\)
a: =-4xyz^2
b: =-9x^2y
c: =16x^2y^2
d: =1/6x^2y^3
e: =13/6x^3y^2
f: =7/12x^4y
a) -xyz² - 3xz.yz
= -xyz² - 3xyz²
= -4xyz²
b) -8x²y - x.(xy)
= -8x²y - x²y
= -9x²y
c) 4xy².x - (-12x²y²)
= 4x²y² + 12x²y²
= 16x²y²
d) 1/2 x²y³ - 1/3 x²y.y²
= 1/2 x²y³ - 1/3 x²y³
= 1/6 x²y³
e) 3xy(x²y) - 5/6 x³y²
= 3x³y² - 5/6 x³y²
= 13/6 x³y²
f) 3/4 x⁴y - 1/6 xy.x³
= 3/4 x⁴y - 1/6 x⁴y
= 7/12 x⁴y