10+5=5

a) \(A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{31.34}\)

\(A=\frac{2}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{31}-\frac{1}{34}\right)\)

\(A=\frac{2}{3}.\left(1-\frac{1}{34}\right)\)

\(A=\frac{2}{3}\cdot\frac{33}{34}=\frac{11}{17}\)

b) \(B=\frac{3}{1}+\frac{3}{3}+\frac{3}{6}+...+\frac{3}{210}\)

\(B=\frac{6}{2}+\frac{6}{6}+\frac{6}{12}+...+\frac{6}{420}\) ( 3/1 = 6/2; 6/6=3/3;..)

\(B=\frac{6}{1.2}+\frac{6}{2.3}+\frac{6}{3.4}+...+\frac{6}{20.21}\)

\(B=6.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{20}-\frac{1}{21}\right)\)

\(B=6.\left(1-\frac{1}{21}\right)=6\cdot\frac{20}{21}=\frac{40}{7}\)

còn ý c với d bn ko bít hả công chúa ori

bài 1 :

A> 13 x 58 x 4 + 32 x 26 x 2 + 52 x 10          ( thay dầu .   =  x   )

   =(13 x 4 ) x 58 + 32 x 13 x 2 x 2 + 13 x 4 x 10

   = ( 13 x 4 ) x 58 + 32 x ( 13 x 2 x 2 )  + ( 13 x 4 ) x 10 

   = 52 x 58 + 32 x 52 + 52 x 10

   =52 x ( 58 + 32 + 10 )

   =52 x 100 =  5200

B>15 x 37 x 4 + 120 x 21 + 21 x 5 x 12

= ( 15 x 4 ) x 37 + 60 x 2 x 21 + 21 x (5 x 12 )

= 60 x 37 + 60 x 42 + 21 x 60

= 60 x ( 37 + 42 + 21 )

= 60 x 100 = 6000

C> 14 x 35 x 5 + 10 x 25 x 7 + 20 x 70 x 2

=   ( 14 x 5 ) x 35 + (10 x 7 ) x 25 + 20 x 70 x 2 

=   70 x 35 + 70 x 25 + 20 x 2 x 70 

=  70 x ( 35 + 25 + 40 )

= 70 x 100 = 7000 

{ câu 3/ hình như thiếu }

\(\frac{x-2}{x-1}=\frac{x+4}{x+7}\)

\(\Leftrightarrow\left(x-2\right)\left(x+7\right)=\left(x-1\right)\left(x+4\right)\)

\(\Leftrightarrow x^2+7x-2x-14=x^2+4x-x-4\)

\(\Leftrightarrow x^2-x^2+7x-2x-4x+x=14-4\)

\(\Leftrightarrow2x=10\)

\(\Leftrightarrow x=5\)

hok tốt!