a) 

(1/3-1/5)x1/4 = 1/3x1/4-1/5x1/4=1/12-1/20=1/30

(1/3-1/5)x1/4 = 2/15x1/4=1/30

b)

2/5 x 3/7 + 2/5 x 4/7= 6/35 + 8/35 = 14/35 = 2/5

2/5 x 3/7 + 2/5 x 4/7= (3/7+4/7) x 2/5 = 1 x 2/5 = 2/5

a: C1: (1/3-1/5)*1/4

=2/15*1/4=2/60=1/30

C2: (1/3-1/5)*1/4

=1/3*1/4-1/5*1/4

=1/12-1/20=1/30

b: C1: 2/5*3/7+2/5*4/7

=6/35+8/35=14/35=2/5

C2: 2/5*3/7+2/5*4/7

=2/5(3/7+4/7)

=2/5*1=2/5

Lời giải:
$S=\frac{1}{7^2}+\frac{2}{7^3}+\frac{3}{7^4}+...+\frac{69}{7^{70}}$

$7S=\frac{1}{7}+\frac{2}{7^2}+\frac{3}{7^3}+...+\frac{69}{7^{69}}$

$6S=7S-S=\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+....+\frac{1}{7^{69}}-\frac{69}{7^{70}}$

$42S=1+\frac{1}{7}+\frac{1}{7^2}+...+\frac{1}{7^{68}}-\frac{69}{7^{69}}$

$\Rightarrow 42S-6S=(1+\frac{1}{7}+\frac{1}{7^2}+...+\frac{1}{7^{68}}-\frac{69}{7^{69}})-(\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+....+\frac{1}{7^{69}}-\frac{69}{7^{70}})$

$\Rightarrow 36S=1-\frac{69}{7^{69}}-\frac{1}{7^{69}}+\frac{69}{7^{70}}$

Hay $36S=1-\frac{69.7-7-69}{7^{70}}=1-\frac{407}{7^{70}}$

$\Rightarrow S=\frac{1}{36}(1-\frac{407}{7^{70}})$

\(=\dfrac{3}{2}-\dfrac{2}{21}-\dfrac{7}{12}+\left[\dfrac{15}{21}-\dfrac{1}{3}+\dfrac{5}{4}-\dfrac{2}{7}-\dfrac{1}{3}\right]\)

=11/12-2/21+5/7-2/3+5/4-2/7

=11/12-2/3+5/4-2/21+3/7

=11/12-8/12+15/12-2/21+9/21

=18/12+7/21

=3/2+1/3

=9/6+2/6=11/6

\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left\{\dfrac{7}{12}-\left[\dfrac{15}{21}-\left(\dfrac{1}{3}-\dfrac{5}{4}\right)-\left(\dfrac{2}{7}+\dfrac{1}{3}\right)\right]\right\}\)

\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left\{\dfrac{7}{12}-\left[\dfrac{15}{21}-\left(-\dfrac{11}{12}\right)-\dfrac{13}{21}\right]\right\}\)

\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left\{\dfrac{7}{12}-\dfrac{85}{84}\right\}\)

\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left(-\dfrac{3}{7}\right)\)

\(B=\dfrac{11}{6}\)

a) 69.(x-157)=18837

  x-157=18837:69

x-157=273

x=273+157

x=430

(x+1)+(x+2)+(x+3)+(x+4)=34

x.4+(1+2+3+4)=34

x.4+10=34

x.4=34-10

x.4=24

x=24:4

x=6

a 69*(x-157)=18837

69*x - 69*157=18837

cùng giảm hai vế đi 69 lần, ta có : 

x-157=18837/69

x-157=273 => x=273+157=430

Vậy x=430

b)x+1+x+2+x+3+x+4 = 34 

x*4 + (1+2+3+4)= 34

x*4 = 24 => x bằng 6

mình mới lên lớp 6 nên viết hơi dài và kém , thông cảm và học tốt nhé !

\(\frac{1}{2}\times\left(x-\frac{4}{5}\right)+\frac{3}{4}x=\frac{5}{12}\)

\(\Leftrightarrow\frac{1}{2}x-\frac{2}{5}+\frac{3}{4}x=\frac{5}{12}\)

\(\Leftrightarrow\frac{1}{2}x+\frac{3}{4}x=\frac{5}{12}+\frac{2}{5}\)

\(\Leftrightarrow\frac{5}{4}x=\frac{49}{60}\)

\(\Leftrightarrow x=\frac{49}{75}\)

Vậy \(x=\frac{49}{75}\)

bạn ơi sao lại có 2/5 vâỵ

phá ngoặc  \(\frac{1}{2}\times\frac{4}{5}=\frac{4}{10}=\frac{2}{5}\)  nhé bạn