Tìm x biết \(\frac{\chi+5}{10}+\frac{\chi+6}{9}=\frac{\chi+7}{8}+\frac{\chi+8}{7}\)
\(\frac{7}{9}\chi\frac{8}{5}-\frac{7}{9}\chi\frac{3}{5}\)
Tính nhanh
\(\frac{7}{9}\cdot\frac{8}{5}-\frac{7}{9}\cdot\frac{3}{5}\)
\(=\frac{7}{9}\left(\frac{8}{5}-\frac{3}{5}\right)\)
\(=\frac{7}{9}\cdot\frac{5}{5}\)
\(=\frac{7}{9}\cdot1=\frac{7}{9}\)
7/9 * 8/5 - 7/9 * 3/5
= 7/9 * ( 8/5 - 3/5 )
= 7/9 * 1
= 7/9
^^ Ủng hộ nha!!!
Tìm x biết \(\frac{x+2}{17}+\frac{x+4}{15}+\frac{x+6}{13}\)\(=\frac{x+8}{11}+\frac{x+10}{9}+\frac{x+12}{7}\)
Giải chi tiết cho tớ nha, tớ tk liền luôn nha!!
\(\frac{2}{6}\)-\(\frac{2}{7}\)+\(\frac{2}{7}\)-\(\frac{2}{8}\)+\(\frac{2}{8}\)-\(\frac{2}{9}\)+..........+\(\frac{2}{\chi\left(\chi+1\right)}\)= \(\frac{2}{9}\)
\(\sqrt[4]{3}.243^{\frac{2\chi+3}{\chi+8}=\frac{1}{9}.9^{\frac{\chi+8}{\chi+2}}}\)
Tìm x biết:\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....\frac{1}{\chi\left(\chi+1\right):2}=\frac{2013}{2015}\)
\(\frac{2}{6}+\frac{2}{12}+...+\frac{2}{x\left(x+1\right)}=\frac{2013}{2015}\)
\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2013}{2015}\)
\(2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2013}{2015}\)
\(2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2013}{2015}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2013}{2015}:2\)
\(\frac{1}{x+1}=\frac{1}{2}-\frac{2013}{4030}\)
\(\frac{1}{x+1}=\frac{1}{2015}\)
=>x+1=2015
=>x=2014
\(\frac{x_1-1}{10}=\frac{x_2-2}{9}=.....=\frac{x_9-9}{2}=\frac{x_{10}-10}{1}\)
và x1+x2+x3+x4+x5+x6+x7+x8+x9+x10=100
Giải chi tiết giúp mk nhé m.n
Mơn m.n nhìu
Áp dụng tc của dãy tỉ số bằng nhau ta có
\(\frac{x_1-1}{10}=.....=\frac{x_{10}-10}{1}=\frac{\left(x_1+x_2+....+x_{10}\right)-\left(1+2+3+...+10\right)}{1+2+3+...+10}\)
\(=\frac{45}{55}=\frac{9}{11}\)
Giải ra ta được
\(x_1=\frac{101}{11}\)
\(x_2=\frac{103}{11}\)
........
\(x_{10}=\frac{119}{11}\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:: \(\frac{x_1-1}{10}=\frac{x_2-2}{9}=...=\frac{x_9-9}{2}=\frac{x_{10}-10}{1}=\frac{x_1-1+x_2-2+...+x_9-9+x_{10}-10}{10+9+...+2+1}\)
\(=\frac{\left(x_1+x_2+..+x_9+x_{10}\right)-\left(1+2+...+9+10\right)}{10+9+...+2+1}=\frac{100-55}{55}=\frac{9}{11}\)
=> \(\frac{x_1-1}{10}=\frac{9}{11}\Leftrightarrow x_1-1=\frac{10\cdot9}{11}\Leftrightarrow x_1=\frac{90}{11}+1=\frac{101}{11}\)
\(\frac{x_2-2}{9}=\frac{9}{11}\Leftrightarrow x_2-2=\frac{9\cdot9}{11}\Leftrightarrow x_2=\frac{81}{11}+2=\frac{103}{11}\)
Tương tự ta cũng có:
\(x_3=\frac{105}{11}\)
\(x_4=\frac{107}{11}\)
\(x_5=\frac{109}{11}\)
\(x_6=\frac{111}{11}\)
\(x_7=\frac{113}{11}\)
\(x_8=\frac{115}{11}\)
\(x_9=\frac{117}{11}\)
\(x_{10}=\frac{119}{11}\)
\(-\frac{1}{2}+\frac{7}{6}+\left(-\frac{7}{8}\right)\))
Giải chi tiết->tick ok?
\(-\frac{1}{2}+\frac{7}{6}+\left(-\frac{7}{8}\right)=-\frac{1}{2}+\frac{7}{6}-\frac{7}{8}\)\(\frac{7}{8}=\frac{-12}{24}+\frac{28}{24}-\frac{21}{24}\)=\(\frac{-12+28-21}{24}=\frac{-5}{24}\)
\(-\frac{1}{2}+\frac{7}{6}+\left(-\frac{7}{8}\right)=\frac{-4}{8}+\frac{7}{6}+\left(\frac{-7}{8}\right)=\frac{-4}{8}+\frac{-7}{8}+\frac{7}{6}=\frac{-11}{8}+\frac{7}{6}=\frac{-33}{24}+\frac{28}{24}=\frac{-5}{24}\)
Cho biểu thức B = \(\left(\frac{x+3}{x-3}+\frac{2\chi^2-6}{9-\chi^2}+\frac{\chi}{\chi+3}\right):\frac{6\chi-12}{2\chi^2-18}\)
a) tìm tập xác định và rút gọn biểu thức
b) Tìm giá trị của B với x=1 hoặc x= -3
c) tìm giá trị nguyên của x để B nhận giá trị nguyên
a, B=[(x+3)/(x-3)+(2x^2-6)/(9-x^2)+x/(x+3)]:[(6x-12)/(2x^2-18)]
=[(x+3)/(x-3)+ -(2x^2-6)/(x^2-9)+x/(x+3)]:[(6x-12)/(2x^2-18)]
=[(x+3)/(x-3)+ -(2x^2-6)/(x-3)(x+3)+x/(x+3)]:[(6x-12)/2(x-3)(x+3)]
={[(x+3)^2-2x^2+6+x(x-3)]/(x-3)(x+3)}:[6(x-2)/2(x-3)(x+3)]
=(x^2+6x+9-2x^2+6+x^2-3x)/(x-3)(x+3): 6(x-2)/2(x-3)(x+3)
=3x+15/(x-3)(x+3): 6(x-2)/2(x-3)(x+3)
=3(x+5)/(x-3)(x+3): 6(x-2)/2(x-3)(x+3
=3(x+5)/(x-3)(x+3).2(x-3)(x+3)/6(x-2)
=3(x+5).6/(x-2)
=6(x+5)/6(x-2)
=x+5/x-2
b,Ta thay : x=1
=>x+5/x-2=1+5/1-2=-6
Ta thay : x=-3
=>x+5/x-2=-3+5/-3-2=-2/5
c, Ta co : x+5/x-2=0
x+5=(x-2).0
x+5=0
x=-5
Vậy : x=-5
hepl me
Tính:\(\frac{\frac{3}{7}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}+\frac{5}{8}-\frac{5}{6}}\)
Giải chi tiết nha
ta có \(\frac{\frac{3}{7}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}=\frac{3\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}{5\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}=\frac{3}{5}\)
và \(\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}+\frac{5}{8}-\frac{5}{6}}=\frac{2\left(\frac{1}{2.2}-\frac{1}{3.2}+\frac{1}{4.2}\right)}{5\left(\frac{1}{4}+\frac{1}{8}-\frac{1}{6}\right)}=\frac{2\left(\frac{1}{4}+\frac{1}{8}-\frac{1}{6}\right)}{5\left(\frac{1}{4}+\frac{1}{8}-\frac{1}{6}\right)}=\frac{2}{5}\)
Vậy \(\frac{\frac{3}{7}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}+\frac{5}{8}-\frac{5}{6}}=\frac{3}{5}+\frac{2}{5}=\frac{5}{5}=1\)
ĐS: 1