Câu 2. (1,5 điểm): Thực hiện các phép tính sau:
a) $(x+2)^2+x(2 x-5)$;
b) $\dfrac{x}{x+3}+\dfrac{2 x}{x-3}+\dfrac{-3 x^2-9}{x^2-9}$ với $x \neq \pm 3$.
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Bài 3:
Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{a}{6}=\dfrac{b}{3}=\dfrac{c}{4}=\dfrac{c-b}{4-3}=10\)
Do đó: a=60; b=30; c=40
Bài 1:
b: \(=\dfrac{x+3-4-x}{x-2}=\dfrac{-1}{x-2}\)
Bài 2:
a: \(=\dfrac{x+1}{2\left(x+3\right)}+\dfrac{2x+3}{x\left(x+3\right)}\)
\(=\dfrac{x^2+x+4x+6}{2x\left(x+3\right)}=\dfrac{x^2+5x+6}{2x\left(x+3\right)}=\dfrac{x+2}{2x}\)
d: \(=\dfrac{3}{2x^2y}+\dfrac{5}{xy^2}+\dfrac{x}{y^3}\)
\(=\dfrac{3y^2+10xy+2x^3}{2x^2y^3}\)
e: \(=\dfrac{x^2+2xy+x^2-2xy-4xy}{\left(x+2y\right)\left(x-2y\right)}=\dfrac{2x^2-4xy}{\left(x+2y\right)\cdot\left(x-2y\right)}=\dfrac{2x}{x+2y}\)
a) \(\dfrac{x^2+2x}{x+2}=\dfrac{x\left(x+2\right)}{x+2}=x\)
b) \(\dfrac{5x+4-3\left(x-2\right)}{3\left(x+5\right)}=\dfrac{5x+4-3x+6}{3\left(x+5\right)}=\dfrac{2x+10}{3\left(x+5\right)}=\dfrac{2\left(x+5\right)}{3\left(x+5\right)}=\dfrac{2}{3}\)
b: \(=\dfrac{x-2+x+6}{\left(x-2\right)\left(x+2\right)}=\dfrac{2}{x-2}\)
`@` `\text {Ans}`
`\downarrow`
`a)`
\(2x(4x²+x-3)\)
`= 2x*4x^2 + 2x*x + 2x*(-3)`
`= 8x^3 + 2x^2 - 6x`
`b)`
\([(-9x)+4x]: (-3x)-3x²\)
`= (-9x) \div (-3x) + 4x \div (-3x) - 3x^2`
`= 3 - 4/3 - 3x^2`
`= 5/3 - 3x^2`
2:
a: x+201=351
=>x=351-201
=>x=150
b: \(8\cdot5^2-27:25\)
\(=8\cdot25-\dfrac{27}{25}\)
\(=200-1,08=198,92\)
d: \(2023-23:\left[9+2\left(2^3-0,21\right)\right]\)
\(=2023-23:\left[9+16-0,42\right]\)
\(=2023-\dfrac{23}{25-0,42}\)
\(=2023-\dfrac{1150}{1229}=\dfrac{2485117}{1229}\)
b: 2(x-21)=84
=>x-21=84/2=42
=>x=42+21=63
c: 135-4(81-x)=55
=>4(81-x)=135-55=80
=>81-x=20
=>x=61
\(x^2\left(y-1\right)-4\left(y-1\right)\\ =\left(y-1\right)\left(x^2-4\right)=\left(y-1\right)\left(x-2\right)\left(x+2\right)\)
Câu 1:
A={1;3;5;7;9}
Câu 2:
A. 24 x 82 + 24 x 18 - 100
= 24 x (82 + 18) - 100
= 24 x 100 - 100
= 2400 - 100 = 2300
B.12 + 3 [ 39 - (5 - 2 )2 ]
= 12 + 3. [39 - 32 ]
= 12 + 3 . [39-9]
= 12 + 3.30
= 12 + 90 = 102
Bài 1:
a, (-33) + 45 + (-67)
= - (33 + 67) + 45
= - 100 + 45
= - 55
c, 75 : [ (153 - 6.52).8 + 20110 ]
= 75 : [ 153 - 312].8 + 1]
= 75 : [ - 159.8 + 1]
= 75 : [-1272 + 1]
= 75 : (-1271)
= - \(\dfrac{75}{1271}\)
Bài 2
6\(x\) + 15 = 75
6\(x\) = 75 - 15
6\(x\) = 60
\(x\) = 60 : 6
\(x\) = 10
a.\(\left(x+2\right)^2+x\left(2x-5\right)\)
=\(x^2+4x+4+2x^2-5x\)
=\(3x^2-x+4\)
b. \(\dfrac{x}{x+3}+\dfrac{2}{x-3}+\dfrac{-3x^2-9}{x^2-9}\)
= \(\dfrac{x\left(x-3\right)}{x^2-9}+\dfrac{2\left(x+3\right)}{x^2-9}+\dfrac{-3x^2-9}{x^2-9}\)
=\(\dfrac{x^2-3x+2x+6-3x^2-9}{x^2-9}\)
=\(\dfrac{-2x^2-x-3}{x^2-9}\)