Thực hiện phép tính :
a, 5/9 : ( 1/11 - 5/22 ) + 5/9 : ( 1/15 - 2/3 )
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chia ra làm các nhóm (13-12+11)+(10-9+8)-(7-6+5) -(4+3+2-1)
hay ta thấy 3 nhóm đầu có tổng =số trừ trong các nhóm đó tức là 12+9-6+(4+3+2-1)
Hay= 23
1: ĐKXĐ: \(x\notin\left\{0;3\right\}\)
\(\dfrac{x+3}{x}-\dfrac{x}{x-3}+\dfrac{9}{x^2-3x}\)
\(=\dfrac{x+3}{x}-\dfrac{x}{x-3}+\dfrac{9}{x\left(x-3\right)}\)
\(=\dfrac{\left(x+3\right)\left(x-3\right)-x^2+9}{x\left(x-3\right)}\)
\(=\dfrac{x^2-9-x^2+9}{x\left(x-3\right)}\)
=0
2: ĐKXĐ: \(x\notin\left\{0;1\right\}\)
\(\dfrac{3}{x}-\dfrac{5}{x-1}+\dfrac{3x+2}{x^2-x}\)
\(=\dfrac{3}{x}-\dfrac{5}{x-1}+\dfrac{3x+2}{x\left(x-1\right)}\)
\(=\dfrac{3x-3-5x+3x+2}{x\left(x-1\right)}\)
\(=\dfrac{x-1}{x\left(x-1\right)}=\dfrac{1}{x}\)
a)27*77+24*27-27=27*(77+24-1)=27*100=2700
b)(-12)+(-9)+121+|-20|=-21+121+20=100+20=120
c)25*101-25*1010=25*101-25*1=25*(101-1)=32*100=3200
\(\frac{\left(-4\right)^6.9^5-\left(-6\right)^9.120.1^{2015}}{8^4.3^{12}-6^{11}.2016^0}=\frac{\left(2^2\right)^6.\left(3^2\right)^5+\left(2.3\right)^9.2^3.3.5.1}{\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}.1}=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\frac{2.6}{3.5}=\frac{4}{5}\)
\(\frac{\left(-4\right)^6.9^5-\left(-6\right)^9.120.1^{2015}}{8^4.3^{12}-6^{11}.2016^0}=\frac{\left(-2\right)^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\frac{2.6}{3.5}=\frac{4}{5}\)
\(\text{Thực hiện phép tính}\)
\(3\text{ × }\left(\frac{1}{7}+\frac{1}{3}-\frac{3}{14}\right) : \frac{11}{4}\)
\(=3\text{ x }\left(\frac{3}{21}+\frac{7}{21}-\frac{3}{14}\right)\text{ : }\frac{11}{4}\)
\(=3\text{ x }\left(\frac{10}{21}-\frac{3}{14}\right)\text{ : }\frac{11}{4}\)
\(=3\text{ x }\left(\frac{140}{294}-\frac{63}{294}\right)\text{ : }\frac{11}{4}\)
\(=3\text{ x }\frac{77}{294}\text{ : }\frac{11}{4}\)
\(=\frac{231}{294}:\frac{11}{4}\)
\(=\frac{231}{294}\text{ x }\frac{4}{11}\)
\(=\frac{924}{3234}=\text{Phân số này có thể rút gọn đó bạn ! Bạn tự rút gọn nha !}\)
\(\left(\frac{21}{8}+\frac{1}{2}\right)\text{ : }\frac{5}{16}\)
\(=\left(\frac{21}{8}+\frac{4}{8}\right)\text{ : }\frac{5}{16}\)
\(=\frac{25}{8}\text{ : }\frac{5}{16}\)
\(=\frac{25}{8}\text{ x }\frac{16}{5}\)
\(=\frac{400}{40}=10\)
1/2*3+1/3*4+1/4*5 + 1/5*6 + .... + 1/99 * 100
= 1/2 -1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 +..... + 1/99 - 1/100
= 1/2 - 1/100
= 49/100 nha bạn !
1/2x3+1/3x4+1/4x5+1/5x6+....+1/99x100
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+....+1/99-1/100
=1/2-1/100=49/100
a)\(\frac{5}{9}:\left(\frac{1}{11}-\frac{5}{22}\right)+\frac{5}{9}:\left(\frac{1}{15}-\frac{2}{3}\right)\)
\(=\frac{5}{9}:\left[\left(\frac{1}{11}-\frac{5}{22}\right)+\left(\frac{1}{15}-\frac{2}{3}\right)\right]\)
\(=\frac{5}{9}:\left[-\frac{3}{22}+-\frac{3}{5}\right]\)
\(=\frac{5}{9}:\frac{-81}{110}\)
\(=\frac{-550}{729}\)