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Giải:
\(\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+...+\dfrac{1}{x.\left(x+2\right)}=\dfrac{16}{99}\)
\(\dfrac{1}{2}.\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{x.\left(x+2\right)}\right)=\dfrac{16}{99}\)
\(\dfrac{1}{2}.\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{x}-\dfrac{1}{x+2}\right)=\dfrac{16}{99}\)
\(\dfrac{1}{2}.\left(\dfrac{1}{3}-\dfrac{1}{x+2}\right)=\dfrac{16}{99}\)
\(\dfrac{1}{3}-\dfrac{1}{x+2}=\dfrac{16}{99}:\dfrac{1}{2}\)
\(\dfrac{1}{3}-\dfrac{1}{x+2}=\dfrac{32}{99}\)
\(\dfrac{1}{x+2}=\dfrac{1}{3}-\dfrac{32}{99}\)
\(\dfrac{1}{x+2}=\dfrac{1}{99}\)
\(\Rightarrow x+2=99\)
\(x=99-2\)
\(x=97\)
Chúc em học tốt!
\(\dfrac{1}{3x5}+\dfrac{1}{5x7}+\dfrac{1}{7x9}+...+\dfrac{1}{x\left(x+2\right)}=\dfrac{16}{99}\)
\(=\dfrac{1}{2}\left(\dfrac{2}{3x5}+\dfrac{2}{5x7}+...+\dfrac{2}{x\left(x+2\right)}\right)=\dfrac{16}{99}\)
\(=\dfrac{2}{3x5}\)\(+\dfrac{2}{5x7}+...+\dfrac{2}{x\left(x+2\right)}=\dfrac{32}{99}\)
\(=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}+.....+\dfrac{1}{x}-\dfrac{1}{x+2}=\dfrac{32}{99}\)
\(=\dfrac{1}{3}-\dfrac{1}{x+2}=\dfrac{32}{99}=>x=97\)
a) \(\dfrac{3}{4}\times x:\dfrac{1}{2}=\dfrac{4}{5}\)
\(\dfrac{3}{4}\times x=\dfrac{4}{5}\times\dfrac{1}{2}\)
\(\dfrac{3}{4}\times x=\dfrac{2}{5}\)
\(x=\dfrac{2}{5}:\dfrac{3}{4}\)
\(x=\dfrac{8}{15}\)
b) \(\left(14-x:6\right)\times7=84\)
\(14-x:6=84:7\)
\(14-x:6=12\)
\(x:6=14-12\)
\(x:6=2\)
\(x=6\times2=12\)
c) \(x\times1,5:2,4=0,3\)
\(x\times1,5=0,3\times2,4\)
\(x\times1,5=0,72\)
\(x=0,72:1,5\)
\(x=0,48\)
d) Thiếu x
x - 5 / 6 = 12 / 7
x = 12 / 7 + 5 / 6
x = 107 / 42
x + 4 / 5 = 8 / 3
x = 8 / 3 - 4 / 5
x = 28 / 15
x * 3 / 9 = 11 / 7 - 3 / 4
x * 3 / 9 = 23 / 28
x = 23 / 28 : 3 / 9
x = 69 / 28
5 / 9 : x = 1 / 3 + 2 / 5
5 / 9 : x = 11 / 15
x = 5 / 9 : 11 / 15
x = 25 / 33
\(1\frac{3}{4}-x=\frac{3}{8}\)
x = 11 / 8
15 , 21 - x = 5 , 6 + 1 , 2
15 , 21 - x = 6 , 8
x = 15 , 21 - 6 , 8
x = 8 , 41
C1 : ( 6 , 75 + 3 , 25 ) * 42
= 10 * 42
= 420
C 2 : ( 6 , 75 + 3 , 25 ) * 42
= 6,75 * 42 + 3,25 * 42
= 283 , 5 + 136 , 5
= 4200
C 1 : ( 9 , 6 - 4 , 2 ) * 3 , 6
= 5 , 4 * 3 , 6
= 19 , 44
C 2 : ( 9 , 6 - 4 , 2 ) * 3 , 6
= 9 , 6 * 3 , 6 - 4 , 2 * 3 , 6
= 34 , 56 - 15 , 12
= 19 , 44
x : 5/4 = 9/5 + 1/2
=> x : 5/4 = 23/10
=> x = 23/10 . 5/4
=> x = 23/8
(x + 3/4) . 5/7 = 10/9
=> x + 3/4 = 10/9 : 5/7
=> x + 3/4 = 14/9
=> x = 14/9 - 3/4
=> x = 29/36
\(x:\frac{5}{4}=\frac{9}{5}+\frac{1}{2}\)
\(\Rightarrow x:\frac{5}{4}=\frac{23}{10}\)
\(\Rightarrow x=\frac{23}{8}\)
0 + 1 + 2 + 3 + 5 + 9 + 7 + 65 + 5 + 0 = x - 56
=> 97 = x - 56
=> x - 56 = 97
x = 97 + 56
x = 153
vậy x = 153
a) = 29/15
b) = 7/15
c) = 1
d) = 3
e) = 67/17
f) = 2
mk nhanh nhất tk cho mk nha
a/\(\frac{3}{5}+\frac{4}{3}=\frac{9}{15}+\frac{20}{15}=\frac{29}{15}\)
b/\(\frac{2}{3}-\frac{1}{5}=\frac{10}{15}-\frac{3}{15}=\frac{7}{15}\)
c/\(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}=\frac{3}{6}+\frac{2}{6}+\frac{1}{6}=\frac{7}{6}\)
d,\(\frac{3}{5}+\frac{4}{7}+\frac{7}{5}+\frac{3}{7}=\left(\frac{3}{5}+\frac{7}{5}\right)+\left(\frac{4}{7}+\frac{3}{7}\right)=2+1=3\)
1 / 5 + x = 3 / 7 + 1 / 3
1 / 5 + x = 16 /21
x = 16 / 21 - 1 / 5
x = 59 / 105
x - 1 / 2 = 2 / 3 - 1 / 5
x - 1 / 2 = 7 / 15
x = 7 / 15 + 1 / 2
x = 29 / 30
3 / 5 * x = 2 / 7+ 1 / 4
3 / 5 * x = 15 / 28
x = 15 / 28 : 3 / 5
x = 25 / 28
7 / 8 : x = 1 / 6 * 2 / 3
7 / 8 : x = 1 / 9
x = 7 / 8 : 1 / 9
x = 63 / 8
\(x:\frac{3}{5}=\frac{4}{7}+\frac{2}{5}\)
=> \(x:\frac{3}{5}=\frac{34}{35}\)
=> \(x=\frac{34}{35}\cdot\frac{3}{5}\)
=> \(x=\frac{102}{175}\)
\(6:x=\frac{3}{7}-\frac{1}{9}\)
=> \(6:x=\frac{20}{63}\)
=> \(x=6:\frac{20}{63}=6\cdot\frac{63}{20}\)
=> \(x=\frac{189}{10}\)