1) thực hiện phép tính
a) \(x-2-\) \(\dfrac{x^2-10}{x+2}\)
b) \(x^2+y^2-\dfrac{2\left(x^4+y^4\right)}{x^2+y^2}\)
Những câu hỏi liên quan
thực hiên phép tính
a.\(\dfrac{x^2+y^2}{4\left(x+y\right)}+\dfrac{2xy}{4\left(x+y\right)}\)
b.\(\dfrac{x+5}{2x-2}-\dfrac{4}{x^2-1}:\dfrac{2}{x+1}\)
a, \(\dfrac{x^2+y^2}{4\left(x+y\right)}+\dfrac{2xy}{4\left(x+y\right)}\)=\(\dfrac{x^2+2xy+y^2}{4\left(x+y\right)}\) = \(\dfrac{\left(x+y\right)^2}{4\left(x+y\right)}\) =\(\dfrac{x+y}{4}\)
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a. \(\dfrac{x^2+y^2}{4\left(x+y\right)}+\dfrac{2xy}{4\left(x+y\right)}\)
\(=\dfrac{x^2+2xy+y^2}{4\left(x+y\right)}\)
\(=\dfrac{\left(x+y\right)^2}{4\left(x+y\right)}\)
\(=\dfrac{x+y}{4}\)
b. \(\dfrac{x+5}{2x-2}-\dfrac{4}{x^2-1}:\dfrac{2}{x+1}\)
\(=\dfrac{x+5}{2\left(x-1\right)}-\dfrac{4}{\left(x+1\right)\left(x-1\right)}:\dfrac{2}{x+1}\)
\(=\dfrac{x+5}{2\left(x-1\right)}-\dfrac{2}{x-1}\)
\(=\dfrac{x+5}{2\left(x-1\right)}-\dfrac{4}{2\left(x-1\right)}\)
\(=\dfrac{x+1}{2\left(x-1\right)}\)
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a) Ta có: \(\dfrac{x^2+y^2}{4\left(x+y\right)}+\dfrac{2xy}{4\left(x+y\right)}\)
\(=\dfrac{x^2+2xy+y^2}{4\left(x+y\right)}\)
\(=\dfrac{\left(x+y\right)^2}{4\left(x+y\right)}\)
\(=\dfrac{x+y}{4}\)
b) Ta có: \(\dfrac{x+5}{2x-2}-\dfrac{4}{x^2-1}:\dfrac{2}{x+1}\)
\(=\dfrac{x+5}{2\left(x-1\right)}-\dfrac{4}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{x+1}{2}\)
\(=\dfrac{x+5}{2\left(x-1\right)}-\dfrac{2}{x-1}\)
\(=\dfrac{x+5}{2\left(x-1\right)}-\dfrac{4}{2\left(x-1\right)}\)
\(=\dfrac{x+5-4}{2\left(x-1\right)}\)
\(=\dfrac{x+1}{2x-2}\)
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Xem thêm câu trả lời
Thực hiện các phép tính sau :
a) left(dfrac{5x+y}{x^2-5xy}+dfrac{5x-y}{x^2+5xy}right).dfrac{x^2-25y^2}{x^2+y^2}
b) dfrac{4xy}{y^2-x^2}:left(dfrac{1}{x^2+2xy+y^2}-dfrac{1}{x^2-y^2}right)
c) left[dfrac{1}{left(2x-yright)^2}+dfrac{2}{4x^2-y^2}+dfrac{1}{left(2x+yright)^2}right].dfrac{4x^2+4xy+y^2}{16x}
d) left(dfrac{2}{x+2}-dfrac{4}{x^2+4x+4}right):left(dfrac{2}{x^2-4}+dfrac{1}{2-x}right)
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Thực hiện các phép tính sau :
a) \(\left(\dfrac{5x+y}{x^2-5xy}+\dfrac{5x-y}{x^2+5xy}\right).\dfrac{x^2-25y^2}{x^2+y^2}\)
b) \(\dfrac{4xy}{y^2-x^2}:\left(\dfrac{1}{x^2+2xy+y^2}-\dfrac{1}{x^2-y^2}\right)\)
c) \(\left[\dfrac{1}{\left(2x-y\right)^2}+\dfrac{2}{4x^2-y^2}+\dfrac{1}{\left(2x+y\right)^2}\right].\dfrac{4x^2+4xy+y^2}{16x}\)
d) \(\left(\dfrac{2}{x+2}-\dfrac{4}{x^2+4x+4}\right):\left(\dfrac{2}{x^2-4}+\dfrac{1}{2-x}\right)\)
Thực hiện phép tínha) ^{dfrac{x^2+2}{x^3-1}} +dfrac{2}{x^2+x+1} +dfrac{1}{1-x}b) dfrac{1}{x+2} +dfrac{3}{x^2-4} +dfrac{x-14}{left(x^2+4x+4right)left(x-2right)}c)dfrac{1}{x-y} -dfrac{3xy}{x^3-y^3} +dfrac{x-y}{x^2+xy+y^2}d) dfrac{1}{a-b} +dfrac{1}{a+b} +dfrac{2a}{a^2+b^2} +dfrac{4a^3}{a^4+b^4}e) dfrac{1}{a^2-a} + dfrac{1}{a^2-3a+2} +dfrac{1}{a^2-5a+6} +dfrac{1}{a^2-7a+12}
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Thực hiện phép tính
a) \(^{\dfrac{x^2+2}{x^3-1}}\) +\(\dfrac{2}{x^2+x+1}\) +\(\dfrac{1}{1-x}\)
b) \(\dfrac{1}{x+2}\) +\(\dfrac{3}{x^2-4}\) +\(\dfrac{x-14}{\left(x^2+4x+4\right)\left(x-2\right)}\)
c)\(\dfrac{1}{x-y}\) -\(\dfrac{3xy}{x^3-y^3}\) +\(\dfrac{x-y}{x^2+xy+y^2}\)
d) \(\dfrac{1}{a-b}\) +\(\dfrac{1}{a+b}\) +\(\dfrac{2a}{a^2+b^2}\) +\(\dfrac{4a^3}{a^4+b^4}\)
e) \(\dfrac{1}{a^2-a}\) + \(\dfrac{1}{a^2-3a+2}\) +\(\dfrac{1}{a^2-5a+6}\) +\(\dfrac{1}{a^2-7a+12}\)
a) \(=\dfrac{x^2+2}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{2}{x^2+x+1}-\dfrac{1}{x-1}=\dfrac{x^2+2+2\left(x-1\right)-\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x^2+2+2x-2-x^2-x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{1}{x^2+x+1}\)
b) \(=\dfrac{1}{x+2}+\dfrac{3}{\left(x-2\right)\left(x+2\right)}+\dfrac{x-14}{\left(x+2\right)^2\left(x-2\right)}=\dfrac{\left(x+2\right)\left(x-2\right)+3\left(x+2\right)+x-14}{\left(x+2\right)^2\left(x-2\right)}=\dfrac{x^2-4+3x+6+x-14}{\left(x+2\right)^2\left(x-2\right)}=\dfrac{x^2+4x-12}{\left(x+2\right)^2\left(x-2\right)}=\dfrac{\left(x-2\right)\left(x+6\right)}{\left(x+2\right)^2\left(x-2\right)}=\dfrac{x+6}{\left(x+2\right)^2}\)
c) \(=\dfrac{x^2+xy+y^2-3xy+\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}=\dfrac{x^2-2xy+y^2+x^2-2xy+y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}=\dfrac{2\left(x^2-2xy+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}=\dfrac{2\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}=\dfrac{2\left(x-y\right)}{x^2+xy+y^2}\)
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SGK Toán 8 tập 1 – Chân trời sáng tạo
23 tháng 7 2023 lúc 15:38
Thực hiện các phép tính sau:
a) \(18{x^4}{y^3}:12{\left( { - x} \right)^3}y\)
b) \({x^2}{y^2} - 2x{y^3}:\left( {\dfrac{1}{2}x{y^2}} \right)\)
a) \(18x^4y^3:12\left(-x\right)^3y\)
\(=\left(18:-12\right)\left(x^4:x^3\right)\left(y^3:y\right)\)
\(=-\dfrac{3}{2}xy^2\)
b) \(x^2y^2-2xy^3:\dfrac{1}{2}xy^2\)
\(=\dfrac{xy^2\left(x-2y\right)}{\dfrac{1}{2}xy^2}\)
\(=\dfrac{x-2y}{\dfrac{1}{2}}\)
\(=2x-4y\)
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23 tháng 12 2022 lúc 16:21
1) Thực hiện các phép tính sau ( giả thiết các phân thức đã cho có nghĩa).a)dfrac{x^3}{x-1}-dfrac{x^2}{x+1}-dfrac{1}{x-1}+dfrac{1}{x+1}b)dfrac{x+y}{2.left(x-yright)}-dfrac{x-y}{2.left(x+yright)}+dfrac{2y^2}{x^2-y^2}c)dfrac{x+5}{2x-4}.dfrac{4-2x}{x+2}d) dfrac{8}{x^2+2x-3}+dfrac{2}{x+3}+dfrac{1}{x-1}Mình đang cần gấp ah
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1) Thực hiện các phép tính sau ( giả thiết các phân thức đã cho có nghĩa).
a)\(\dfrac{x^3}{x-1}\)-\(\dfrac{x^2}{x+1}\)-\(\dfrac{1}{x-1}\)+\(\dfrac{1}{x+1}\)
b)\(\dfrac{x+y}{2.\left(x-y\right)}\)-\(\dfrac{x-y}{2.\left(x+y\right)}\)+\(\dfrac{2y^2}{x^2-y^2}\)
c)\(\dfrac{x+5}{2x-4}\).\(\dfrac{4-2x}{x+2}\)
d) \(\dfrac{8}{x^2+2x-3}\)+\(\dfrac{2}{x+3}\)+\(\dfrac{1}{x-1}\)
Mình đang cần gấp ah
a.
\(\dfrac{x^3}{x-1}-\dfrac{x^2}{x+1}-\dfrac{1}{x-1}+\dfrac{1}{x+1}=\dfrac{x^3-1}{x-1}-\dfrac{x^2-1}{x+1}\)
\(=\dfrac{\left(x-1\right)\left(x^2+x+1\right)}{x-1}-\dfrac{\left(x-1\right)\left(x+1\right)}{x+1}\)
\(=x^2+x+1-\left(x-1\right)=x^2+2\)
b.
\(\dfrac{x+y}{2\left(x-y\right)}-\dfrac{x-y}{2\left(x+y\right)}+\dfrac{2y^2}{x^2-y^2}\)
\(=\dfrac{\left(x+y\right)^2}{2\left(x-y\right)\left(x+y\right)}-\dfrac{\left(x-y\right)^2}{2\left(x-y\right)\left(x+y\right)}+\dfrac{4y^2}{2\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{\left(x+y\right)^2-\left(x-y\right)^2+4y^2}{2\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{4xy+4y^2}{2\left(x-y\right)\left(x+y\right)}=\dfrac{4y\left(x+y\right)}{2\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{2y}{x-y}\)
c.
\(\dfrac{x+5}{2x-4}.\dfrac{4-2x}{x+2}=\dfrac{x+5}{2x-4}.\dfrac{-\left(2x-4\right)}{x+2}=-\dfrac{x+5}{x+2}\)
d.
\(\dfrac{8}{x^2+2x-3}+\dfrac{2}{x+3}+\dfrac{1}{x-1}=\dfrac{8}{\left(x-1\right)\left(x+3\right)}+\dfrac{2\left(x-1\right)}{\left(x-1\right)\left(x+3\right)}+\dfrac{x+3}{\left(x-1\right)\left(x+3\right)}\)
\(=\dfrac{8+2\left(x-1\right)+x+3}{\left(x-1\right)\left(x+3\right)}=\dfrac{3x+9}{\left(x-1\right)\left(x+3\right)}\)
\(=\dfrac{3\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}=\dfrac{3}{x-1}\)
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Thực hiện phép tính:
\(a,\left(x-\dfrac{x^2+y^2}{x+y}\right)\left(\dfrac{1}{y}+\dfrac{2}{x-y}\right)\)
\(b,\left(\dfrac{2}{x^2-1}+\dfrac{x^2-3}{3x^2-1}\right):\left[\dfrac{1}{x}-\dfrac{2x\left(x^2-3\right)}{\left(x^2-1\right)\left(3x^2-1\right)}\right]\)
BT10: Thực hiện phép tínha,-xyz^2-3xz.yzb,-8x^2y-x.left(xyright)c,4xy^2 .x-left(-12x^2y^2right)d,dfrac{1}{2}x^2y^3-dfrac{1}{3}x^2y.y^2e,3xyleft(x^2yright)-dfrac{5}{6}x^3y^2f,dfrac{3}{4}x^4y-dfrac{1}{6}xy.x^3
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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
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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
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18 tháng 2 2021 lúc 13:37
Bài 1: (4 điểm) Thực hiện phép tính:
a/ \(\dfrac{x-1}{x+1}-\dfrac{x+1}{x-1}+\dfrac{4}{x^2-1}\) b/ \(\dfrac{x^3y+xy^3}{x^4y}:\left(x^2+y^2\right)\)
a) \(\dfrac{x^2-2x+1-x^2-2x-1+4}{\left(x+1\right)\left(x-1\right)}=\dfrac{-4\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}=\dfrac{-4}{x+1}\)
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\(\dfrac{xy\left(x^2+y^2\right)}{xy\left(x^3\right)}.\dfrac{1}{x^2+y^2}=\dfrac{1}{x^3}\)
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a) Ta có: \(\dfrac{x-1}{x+1}-\dfrac{x+1}{x-1}+\dfrac{4}{x^2-1}\)
\(=\dfrac{\left(x-1\right)^2}{\left(x+1\right)\left(x-1\right)}-\dfrac{\left(x+1\right)^2}{\left(x+1\right)\left(x-1\right)}+\dfrac{4}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x^2-2x+1-x^2-2x-1+4}{\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{-4x+4}{\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{-4\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}=\dfrac{-4}{x+1}\)
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Làm các phép tính sau :
a) \(\left(\dfrac{x^2}{y^2}+\dfrac{y}{x}\right):\left(\dfrac{x}{y^2}-\dfrac{1}{y}+\dfrac{1}{x}\right)\)
b) \(\left(\dfrac{1}{x^2+4x+4}-\dfrac{1}{x^2-4x+4}\right):\left(\dfrac{1}{x+2}-\dfrac{1}{x-2}\right)\)
Bài 1. Thực hiện các phép tính saua) xy(3x-2y)-2xy^2b) (x^2 +4x+4):(x+2)cdfrac{2left(x-1right)}{x^2}.dfrac{x}{left(x-1right)}Bài 2.phân tích các đa thức sau thành nhân tử a)2x^2-4x+2 b)x^2-y^2+3x-3y
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Bài 1. Thực hiện các phép tính sau
a) xy(3x-2y)-2\(xy^2\)
b) (\(x^2\) +4x+4):(x+2)
c\(\dfrac{2\left(x-1\right)}{x^2}.\dfrac{x}{\left(x-1\right)}\)
Bài 2.phân tích các đa thức sau thành nhân tử
a)\(2x^2\)-4x+2 b)\(x^2-y^2+3x-3y\)
B1: a)\(xy\left(3x-2y\right)-2xy^2=3x^2y-2y^2x-2xy^2=3x^2y-4xy^2\)
b) \(\left(x^2+4x+4\right):\left(x+2\right)=\left(x+2\right)^2:\left(x+2\right)=\left(x+2\right)\)
\(\dfrac{2\left(x-1\right)}{x^2}.\dfrac{x}{\left(x-1\right)}=\dfrac{2\left(x-1\right)x}{x^2\left(x-1\right)}=\dfrac{2}{x}\)
B2:
a)\(2x^2-4x+2=2\left(x^2-2x+1\right)=2\left(x-1\right)^2\)
b)\(x^2-y^2+3x-3y=\left(x-y\right)\left(x+y\right)+3\left(x-y\right)=\left(x-y\right)\left(x+y+3\right)\)
Mấy bài này là mấy bài rất rất rất cơ bản, học sinh TB cũng phải tự làm được, mấy bài kiểu này đừng nên đăng lên hỏi nha:vv
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