a) Ta có: \(\frac{\frac{4}{17}-\frac{4}{177}-\frac{4}{1779}}{\frac{5}{17}-\frac{5}{177}-\frac{5}{1779}}=\frac{4.\left(\frac{1}{7}-\frac{1}{177}-\frac{1}{1779}\right)}{5.\left(\frac{1}{7}-\frac{1}{177}-\frac{1}{1779}\right)}=\frac{4}{5}\)

b) \(\frac{1330}{1331}-\frac{7}{1.8}-\frac{19}{8.27}-.....-\frac{331}{1000.1331}\)

\(=\frac{1330}{1331}-\left(\frac{8-7}{1.8}+\frac{27-8}{8.27}+.....+\frac{1331-1000}{1000.1331}\right)\)

\(=\frac{1330}{1331}-\left(1-\frac{1}{8}+\frac{1}{8}-\frac{1}{27}+....+\frac{1}{1000}-\frac{1}{1331}\right)\)

\(=\frac{1330}{1331}-\left(1-\frac{1}{1331}\right)\)

\(=\frac{1330}{1331}-\frac{1330}{1331}=0\)

Vậy \(\frac{1330}{1331}-\frac{7}{1.8}-\frac{19}{8.27}-....\frac{331}{1000.1331}=0\)

CHÚC BẠN HỌC TỐT

a) \(\frac{\frac{4}{17}-\frac{4}{177}-\frac{4}{1779}}{\frac{5}{17}-\frac{5}{177}-\frac{5}{1779}}\)

\(=\frac{4\left(\frac{1}{17}-\frac{1}{177}-\frac{1}{1779}\right)}{5\left(\frac{1}{17}-\frac{1}{177}-\frac{1}{1779}\right)}\)

\(=\frac{4}{5}\)

 bÀI LÀM

a) x⁴+x³+2x²+x+1=(x⁴+x³+x²)+(x²+x+1)=x²(x²+x+1)+(x²+x+1)=(x²+x+1)(x²+1)

b)a³+b³+c³-3abc=a³+3ab(a+b)+b³+c³ -(3ab(a+b)+3abc)=(a+b)³+c³-3ab(a+b+c)

=(a+b+c)((a+b)²-(a+b)c+c²)-3ab(a+b+c)=(a+b+c)(a²+2ab+b²-ac-ab+c²-3ab)=(a+b+c)(a²+b²+c²-ab-ac-bc)

c)Đặt x-y=a;y-z=b;z-x=c

a+b+c=x-y-z+z-x=o

đưa về như bài b

d)nhóm 2 hạng tử đầu lại và 2hangj tử sau lại để 2 hạng tử sau ở trong ngoặc sau đó áp dụng hằng đẳng thức dề tính sau đó dặt nhân tử chung

e)x²(y-z)+y²(z-x)+z²(x-y)=x²(y-z)-y²((y-z)+(x-y))+z²(x-y)

=x²(y-z)-y²(y-z)-y²(x-y)+z²(x-y)=(y-z)(x²-y²)-(x-y)(y²-z²)=(y-z)(x²-2y²+xy+xz+yz)

\(\frac{m}{n}=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{1331}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1330}\right)\)

\(\frac{m}{n}=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{1330}+\frac{1}{1331}\right)-2.\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1330}\right)\)

\(\frac{m}{n}=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{1330}+\frac{1}{1331}\right)-\left(1+\frac{1}{2}+...+\frac{1}{665}\right)\)

\(\frac{m}{n}=\frac{1}{666}+\frac{1}{667}+...+\frac{1}{1330}+\frac{1}{1331}\)

\(\frac{m}{n}=\left(\frac{1}{666}+\frac{1}{1331}\right)+\left(\frac{1}{667}+\frac{1}{1330}\right)+...+\left(\frac{1}{998}+\frac{1}{999}\right)\)

\(\frac{m}{n}=\frac{1997}{666.1331}+\frac{1997}{667.1330}+...+\frac{1997}{998.999}=\frac{1997k_1+1997.k_2+...+1997.k_{333}}{666.667...1331}\)

\(\frac{m}{n}=\frac{1997.\left(k_1+k_2+...+k_{333}\right)}{666.667...1330.1331}\) trong đó: k₁;...; k₃₃₃ là các thừa số phụ của các phân số trong tổng 

Nhận xét: phân số trên có tử chia hết cho 1997 là số nguyên tố; mẫu số không chia hết cho thừa số nguyên tố 1997 nên khi rút gọn tử vẫn chia hết cho 1997

=> m chia hết cho 1997

\(\frac{7}{13}.\frac{5}{19}+\frac{7}{19}.\frac{8}{13}-\frac{37}{19}=\frac{1}{19}\left(\frac{5.7}{13}+\frac{7.8}{13}-37\right)=\frac{1}{19}\left(\frac{91}{13}-37\right)=\frac{1}{19}.\left(-30\right)=-\frac{30}{19}\)

\(=\frac{4x3x7x\left(-20\right)x\left(-11\right)}{7x5x4x12}=\frac{4x3x7x5x4x11}{7x5x4x3x4}=11\)

$=\frac{4x3x7x\left(-20\right)x\left(-11\right)}{7x5x4x12}=\frac{4x3x7x5x4x11}{7x5x4x3x4}=11$

\(\left(\frac{2}{9}+\frac{7}{9}\right)+\left(\frac{1}{5}+\frac{4}{5}\right)=1+1=2\)\(2\)

\(\frac{19}{37}+1-\frac{19}{37}=\left(\frac{19}{37}-\frac{19}{37}\right)+1=1\)

=2 nha bn mk bấm nhầm

\(B=1\frac{6}{41}.\left(\frac{12+\frac{12}{19}+\frac{12}{37}-\frac{12}{53}}{3+\frac{3}{19}+\frac{3}{37}-\frac{3}{53}}\right):\left(\frac{4+\frac{4}{19}+\frac{4}{37}-\frac{4}{53}}{5+\frac{5}{19}+\frac{5}{37}-\frac{5}{53}}\right).\frac{124242423}{237373735}\)

\(B=1\frac{6}{41}.\left[\frac{12\left(\frac{1}{19}+\frac{1}{37}-\frac{1}{53}\right)}{3\left(\frac{1}{19}+\frac{1}{37}-\frac{1}{53}\right)}\right]:\left[\frac{4\left(\frac{1}{19}+\frac{1}{37}-\frac{1}{53}\right)}{5\left(\frac{1}{19}+\frac{1}{37}-\frac{1}{53}\right)}\right].\frac{124242423}{237373735}\)

\(B=1\frac{6}{41}\left(\frac{12}{3}.\frac{5}{4}\right).\frac{124242423}{237373735}\)

\(B=1\frac{6}{41}.5.\frac{123}{235}\)

\(B=\frac{47.5.123}{41.235}=\frac{47.5.41.3}{41.5.47}=3\)

B=\(1\frac{6}{41}.\left(\frac{12+\frac{12}{19}+\frac{12}{37}-\frac{12}{53}}{3+\frac{3}{19}+\frac{3}{37}-\frac{3}{53}}:\frac{4+\frac{4}{19}+\frac{4}{37}-\frac{4}{53}}{5+\frac{5}{19}+\frac{5}{37}-\frac{5}{53}}\right).\frac{124242423}{237373735}\)

B=\(\frac{47}{41}.\left(\frac{12.\left(1+\frac{1}{19}+\frac{1}{37}-\frac{1}{53}\right)}{3.\left(1+\frac{1}{19}+\frac{1}{37}-\frac{1}{53}\right)}:\frac{4.\left(1+\frac{1}{19}+\frac{1}{37}-\frac{1}{53}\right)}{5.\left(1+\frac{1}{19}+\frac{1}{37}-\frac{1}{53}\right)}\right).\frac{123.1010101}{235.1010101}\)

B=\(\frac{47}{41}.\left(\frac{12}{3}:\frac{4}{5}\right).\frac{123}{235}=\frac{47}{41}.\left(\frac{12}{3}.\frac{5}{4}\right).\frac{123}{235}\)

B=\(\frac{47}{41}.\frac{15}{3}.\frac{123}{235}=\frac{47.5.3.41.3}{41.3.5.47}=3\)

Vậy B=3

Chúc bn học tốt

\(B=1\frac{6}{41}\left(\frac{12+\frac{12}{19}+\frac{12}{37}-\frac{12}{53}}{3+\frac{3}{19}+\frac{3}{27}-\frac{3}{53}}:\frac{4+\frac{4}{19}+\frac{4}{37}-\frac{4}{53}}{5+\frac{5}{19}+\frac{5}{37}-\frac{5}{53}}\right)\cdot\frac{124242423}{237373735}\)

\(B=\frac{47}{6}\cdot\left(\frac{12\left(1+\frac{1}{19}+\frac{1}{37}-\frac{1}{53}\right)}{3\left(1+\frac{1}{19}+\frac{1}{27}-\frac{1}{53}\right)}:\frac{4\left(1+\frac{1}{19}+\frac{1}{37}-\frac{1}{53}\right)}{5\left(1+\frac{1}{19}+\frac{1}{37}-\frac{1}{53}\right)}\right)\cdot\frac{123\cdot1010101}{235\cdot1010101}\)

\(B=\frac{47}{6}\cdot\left(4:\frac{4}{5}\right)\cdot\frac{123}{235}\)

\(B=\frac{47}{6}\cdot5\cdot\frac{123}{235}\)

\(B=3\)

WHat?

t tưởng mọi hôm bài này m làm thạo lắm mà bây h chịu ak

giỏi thi làm đi

\(B=-1\frac{1}{5}\cdot\frac{4\left(3+\frac{1}{3}-\frac{3}{7}-\frac{3}{53}\right)}{3+\frac{1}{3}-\frac{3}{7}-\frac{3}{53}}\div\frac{4+\frac{4}{17}+\frac{4}{19}+\frac{4}{2003}}{5+\frac{5}{17}+\frac{5}{19}+\frac{5}{2003}}\)

\(B=\frac{-6}{5}\cdot4\div\frac{4\left(1+\frac{1}{17}+\frac{1}{19}+\frac{1}{2003}\right)}{5\left(1+\frac{1}{17}+\frac{1}{19}+\frac{1}{2003}\right)}\)

\(B=\frac{-24}{5}\div\frac{4}{5}\)

\(B=-6\)

\(B=-1\frac{1}{5}.\frac{4.\frac{3}{7}}{\frac{3}{37}}:\frac{4+3.\frac{4}{1}}{5+3.\frac{5}{1}}\)

\(B=-\frac{6}{5}.\frac{148}{7}:\frac{4}{5}\)

\(B=-\frac{222}{7}\)

GIÚP ĐỠ MỚI 

nguyễnCôngBắcKỳ_6a1, bài này còn cần nữa k, mik lm cho

Bài làm

\(A=1\frac{6}{41}.\left(\frac{12+\frac{12}{19}+\frac{12}{37}-\frac{12}{53}}{3+\frac{3}{19}+\frac{3}{37}-\frac{3}{53}}:\frac{4+\frac{4}{19}+\frac{4}{37}-\frac{4}{53}}{5+\frac{4}{19}+\frac{4}{37}-\frac{4}{53}}\right).\frac{124242423}{237373735}\)

\(A=\frac{47}{41}.\left(\frac{12+12.\frac{1}{19}+12.\frac{1}{37}-12.\frac{1}{53}}{3+3.\frac{1}{19}+3.\frac{1}{37}-3.\frac{1}{53}}:\frac{4+4.\frac{1}{19}+4.\frac{1}{37}-4.\frac{1}{53}}{5+4.\frac{1}{19}+4.\frac{1}{37}-4.\frac{1}{53}}\right).\frac{124242423}{237373735}\)

\(A=\frac{47}{41}.\left(\frac{12.\left(1+\frac{1}{19}+\frac{1}{37}-\frac{1}{53}\right)}{3.\left(1+\frac{1}{19}+\frac{1}{37}-\frac{1}{53}\right)}:\frac{4.\left(\frac{1}{19}+\frac{1}{37}-\frac{1}{53}\right)+1}{5.4.\left(\frac{1}{19}+\frac{1}{37}-\frac{1}{53}\right)}\right).\frac{124242423}{237373735}\)

\(A=\frac{47}{41}.\left(\frac{12.1}{3.1}:\frac{4.+1}{5.4.}\right).\frac{124242423}{237373735}\)

\(A=\frac{47}{41}.\left(\frac{12}{3}:\frac{5}{20.}\right).\frac{124242423}{237373735}\)

\(A=\frac{47}{41}.\left(\frac{12}{3}x\frac{20}{5}\right).\frac{124242423}{237373735}\)

\(A=\frac{47}{41}.\frac{80}{5}.\frac{124242423}{237373735}\)

\(A=\frac{47}{41}.16.\frac{124242423}{237373735}\)

~ Đến đây tự tính tiếp, bn rút gọn tử phân số \(\frac{124242423}{237373735}\)này thử xem, mik k chắc là rút gọn đc, xg bn tính như bình thường nhé ~
# Chúc bạn học tốt #

\(\frac{5}{23}x\frac{17}{6}+\frac{5}{23}x\frac{9}{26}\)

\(=\frac{5}{23}x\left(\frac{17}{26}+\frac{9}{26}\right)\)

\(=\frac{5}{23}x1=\frac{5}{23}\)