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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: \(x\left(x-y\right)+y\left(x+y\right)\)
\(=x^2-xy+xy+y^2\)
\(=x^2+y^2\)
=100
b: \(x\left(x^2-y\right)-x^2\left(x+y\right)+y\left(x^2-x\right)\)
\(=x^3-xy-x^3-x^2y+x^2y-xy\)
\(=-2xy\)
Bài 1:
\(a.8,32+14,76+5,24=8,32+\left(14,76+5,24\right)\)
\(=8,32+20=28,32\)
\(b,16,88+9,76+3,12=\left(16,88+3,12\right)+9,76\)
\(=20+9,76=29,76\)
\(c,\left(\dfrac{2}{5}+\dfrac{7}{9}\right)+\dfrac{3}{5}=\left(\dfrac{2}{5}+\dfrac{3}{5}\right)+\dfrac{7}{9}\)
\(=1+\dfrac{7}{9}=\dfrac{16}{9}\)
\(d,\dfrac{19}{11}+\left(\dfrac{8}{13}+\dfrac{3}{11}\right)\)
\(=\left(\dfrac{19}{11}+\dfrac{3}{11}\right)+\dfrac{8}{13}=\dfrac{22}{11}+\dfrac{8}{13}\)
\(=2+\dfrac{8}{13}=\dfrac{34}{13}\)
bài 9 :
Bài giải:
a) 5 . 42 – 18 : 32 = 5 . 16 - 18 : 9 = 80 - 2 = 78;
b) 33 . 18 – 33 . 12 = 27 . 18 - 27 . 12 = 486 - 324 = 162;
Lưu ý. Có thể áp dụng tính chất phân phối của phép nhân đối với phép cộng:
33 . 18 – 33 . 12 = 33 (18 - 12) = 27 . 6 = 162;
c) 39 . 213 + 87 . 39 = 39 . (213 + 87) = 39 . 300 = 11700;
d) 80 – [130 – (12 – 4)2] = 80 - (130 - 64) = 80 - 66 = 14.
Bài 113:
Tìm 1 số có 3 chữ số khác nhau biết số đó gấp 39 lần tổng các chữ số của nó .
a: \(\left(\dfrac{x+2}{x+1}-\dfrac{2x}{x-1}\right)\cdot\dfrac{3x+3}{x}+\dfrac{4x^2+x+7}{x^2-x}\)
\(=\dfrac{x^2+x-2-2x^2-2x}{\left(x+1\right)\left(x-1\right)}\cdot\dfrac{3\left(x+1\right)}{x}+\dfrac{4x^2+x+7}{x\left(x-1\right)}\)
\(=\dfrac{-x^2-x-2}{x-1}\cdot\dfrac{3}{x}+\dfrac{4x^2+x+7}{x\left(x-1\right)}\)
\(=\dfrac{-3x^2-3x-6+4x^2+x+7}{x\left(x-1\right)}=\dfrac{x^2-2x+1}{x\left(x-1\right)}=\dfrac{x-1}{x}\)
Bài 1:
a)\(\frac{2}{3}.\frac{5}{2}-\frac{3}{4}.\frac{2}{3}=\frac{5}{3}-\frac{1}{2}=\frac{7}{6}\)
b)\(2.\left(\frac{-3}{2}\right)^2-\frac{7}{2}=\frac{2.9}{4}-\frac{7}{2}=\frac{9-7}{2}=\frac{2}{2}=1\)
c)\(-\frac{3}{4}.\frac{68}{13}-0,75.\frac{36}{13}=\frac{-3.4.17}{4.13}-\frac{3.9.4}{4.13}=\frac{-51-27}{13}=\frac{-78}{13}=-6\)
Bài 2:
a)|x-1,4|=1,6
\(\Rightarrow\left[\begin{array}{nghiempt}x-1,4=1,6\\x-1,4=-1,6\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=3\\x=-0,2\end{array}\right.\)
b) \(\frac{3}{4}-x=\frac{4}{5}\)
\(x=\frac{3}{4}-\frac{4}{5}=-\frac{1}{20}\)
c)(1-2x)3=-8
(1-2x)3=(-2)3
1-2x=-2
2x=3
x=\(\frac{3}{2}\)
Bài 3:
\(\frac{x}{2}=\frac{y}{5}=\frac{z}{7}=k\)
\(\Rightarrow\begin{cases}x=2k\\y=5k\\z=7k\end{cases}\)
A=\(\frac{2k-5k+7k}{2k+2.5k-7k}=\frac{4k}{5k}=\frac{4}{5}\)
=> x=4/5 . 2= 8/5
y=4/5 . 5=4
z=4/5.7=28/5
a: \(=\dfrac{4x-2+6x^2-6x+2x^2+1}{2x\left(2x-1\right)}=\dfrac{8x^2-2x-1}{2x\left(2x-1\right)}\)
\(=5x^3-5x^2y+5x-2x^2y+2xy^2-2y\)
\(=5x^3-7x^2y+2xy^2+5x-2y\)
Bài 2:
\(1)25-12\cdot2+2^3\\ =25-24+2^3\\ =1+8\\ =9\\ 2)45-12\cdot3+2^3\\ =45-36+2^3\\ =9+8\\ =17\\ 3)32+5\cdot13-3\cdot2^3\\ =32+65-3\cdot8\\ =97-24\\ =73\\ 4)150+50:5-2\cdot3^2\\ =150+10-2\cdot9\\ =160-18\\ =142\\ 5)35-2\cdot1^{111}+3\cdot7^2\\ =35-2\cdot1+3\cdot49\\ =35-2+147\\ =33+147\\ =180\\ 6)2023-5^3:25+27\\ =2023-125:25+27\\ =2023-5+27\\ =2023+22\\ =2045\)
Bài 1:
1: \(3^2\cdot5^3+9^2=9\cdot125+81=1206\)
2: \(55+45:3^2=55+45:9=55+5=60\)
3: \(8^3:4^2-5^2=\dfrac{2^6}{2^4}-25=2^2-25=4-25=-21\)
4: \(5\cdot3^2-32:2^2=5\cdot9-2^3=45-8=37\)
5: \(16:2^3+5^2\cdot4=16:8+25\cdot4=2+100=102\)
6: \(5\cdot2^2-18:3^2=5\cdot4-18:9=20-2=18\)
7: \(3\cdot5^2-15\cdot2^2=3\cdot25-15\cdot4=75-60=15\)
8: \(2^3\cdot6-72:3^2=8\cdot6-72:9=48-8=40\)
9: \(5\cdot2^2-27:3^2=5\cdot4-27:9=20-3=17\)
10: \(3\cdot2^4+81:3^2=3\cdot16+81:9=48+9=57\)
11: \(4\cdot5^3-32:2^5=4\cdot125-32:32=500-1=499\)
12: \(6\cdot5^2-32:2^4\)
\(=6\cdot25-32:16\)
=150-2=148
Bài 3:
1: \(2^8:2^4+3^2\cdot3\)
\(=2^4+3^3\)
=16+27=43
2: \(3^{24}:3^{21}+2^2\cdot2^3\)
\(=3^3+2^5\)
=27+32=59
3: \(5^9:5^7+12\cdot3+7^0\)
\(=5^2+4+1\)
=25+5=30
4: \(5^6:5^4+3^2-2021^0\)
\(=5^2+9-1\)
=25+8=33
5: \(3^{19}:3^{16}+5^2\cdot2^3-1^{2021}\)
\(=3^3+25\cdot8-1\)
=200+26=226
6: \(3^6:3^5+2\cdot2^3+2021^0\)
\(=3+2^4+1\)
=4+16=20