\(3\frac{3}{4}\times4=\frac{3\times4+3}{4}\times4=\frac{15}{4}\times4=\frac{15\times4}{4}=15\)

\(4\frac{3}{2}\div1\frac{1}{2}=\frac{4\times2+3}{2}\div\frac{1\times2+1}{2}=\frac{11}{2}\div\frac{3}{2}=\frac{11}{2}\times\frac{2}{3}=\frac{11}{3}\)

\(4\frac{3}{4}+2\frac{3}{2}=\frac{4\times4+3}{4}+\frac{2\times2+3}{2}=\frac{19}{4}+\frac{7}{2}=\frac{19}{4}+\frac{14}{4}=\frac{33}{4}\)

\(3\frac{8}{6}-4\frac{1}{3}=\frac{3\times8+6}{6}-\frac{4\times3+1}{3}=\frac{30}{6}-\frac{13}{3}=\frac{30}{6}-\frac{26}{6}=\frac{4}{6}=\frac{2}{3}\)

\(3\frac{2}{4}\)x 4 = \(\frac{14}{4}\)x 4 = \(\frac{56}{4}\)

\(4\frac{3}{2}\): \(1\frac{1}{2}\)= \(\frac{11}{2}\): \(\frac{3}{2}\)= \(\frac{11}{2}\)x \(\frac{2}{3}\)= \(\frac{22}{6}\)= \(\frac{11}{3}\)

\(4\frac{3}{4}\)+ \(2\frac{3}{2}\)= \(\frac{11}{4}\)+ \(\frac{7}{2}\)= \(\frac{25}{4}\)= 6,25

\(3\frac{8}{6}\)- \(4\frac{1}{3}\)= \(\frac{13}{3}\)- \(\frac{13}{3}\)= 0

 \(\dfrac{3}{4}\times\dfrac{8}{5}:1\dfrac{1}{6}\) 

=\(\dfrac{6}{5}:\) \(\dfrac{7}{6}\) 

=\(\dfrac{6}{5}\times\dfrac{6}{7}=\dfrac{36}{35}\)

2\(\dfrac{1}{3}\) x 1\(\dfrac{1}{4}\) -\(\dfrac{7}{5}\)

\(\dfrac{7}{3}\times\dfrac{5}{4}-\) \(\dfrac{7}{5}\) 

\(\dfrac{35}{12}-\dfrac{7}{5}\)

\(\dfrac{175}{60}-\dfrac{84}{60}=\dfrac{91}{60}\)

4\(\dfrac{2}{3}+1\dfrac{1}{4} +2\dfrac{1}{3}+2\dfrac{3}{7}\)

(4 +2) + \(\left(\dfrac{2}{3}+\dfrac{1}{3}\right)\) +1\(\dfrac{1}{4}\) + \(2\dfrac{3}{7}\) 

6 + 1 + \(\dfrac{5}{4}\) + \(\dfrac{17}{7}\)

7 + \(\dfrac{103}{28}\)

\(\dfrac{299}{28}\)

Tử số của A là :

\(1+\left(\frac{2007}{2}+1\right)+\left(\frac{2006}{3}+1\right)+...+\left(\frac{1}{2008}+1\right)\)

\(=\frac{2009}{2009}+\frac{2009}{2}+\frac{2009}{3}+...+\frac{2009}{2008}\)

\(=2009.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2009}\right)\)

Tử số của A là 2009 . Mẫu số 

Vậy A = 2009

uNGR HỘ NHA

a.5/6 - 26/5 X 1/13 = 13/30

b.( 19/23 - 22/46 ) X 23/46 = 3/23

c.25/8 x 14/30 = 35/24

d.( 3/4 x 5/7 ) x ( 20/9 x 14/15 ) = 10/9

e.4/35 x 25/32 x 38/24 = 95/672

g. 1/2 x 3/4 x 2/3 x 4/5 = 1/5

h.5/6 x 11/4 - 5/4 x 23/6 = -5/2

i.9/16 x 13/4 - 9/4 x 5/16 + 9/16 x 17/4 = 225/64

k.( 7 x 1/3 ) x ( 1/7 x 6 ) = 2

m.2/3 x ( 3/5 + 3/7 ) = 34/35

n.4/5 x ( 5/8 + 7/4 ) = 19/10

p.( 1/33 + 31/333 - 341/3333 ) x ( 1/2 - 1/3 - 1/6 ) = 0

mih giành cả nửa tiếng để giải đó , k nha

ghi ca cach lam nhe

\(\frac{2}{3}.\frac{4}{5}+\frac{1}{3}.\frac{4}{5}=\frac{4}{5}\left(\frac{2}{3}+\frac{1}{3}\right)=\frac{4}{5}.\frac{3}{3}=\frac{4}{5}.1=\frac{4}{5}\)

\(\frac{1}{2}:\frac{3}{4}+\frac{1}{6}:\frac{3}{4}=\frac{3}{4}:\left(\frac{1}{2}+\frac{1}{6}\right)=\frac{3}{4}:\frac{2}{3}=\frac{9}{8}\)

\(\frac{2}{3}.\frac{4}{5}-\frac{1}{3}.\frac{4}{5}=\frac{4}{5}\left(\frac{2}{3}-\frac{1}{3}\right)=\frac{4}{5}.\frac{1}{3}=\frac{4}{15}\)

\(\frac{1}{2}:\frac{3}{4}-\frac{1}{6}:\frac{3}{4}=\frac{3}{4}:\left(\frac{1}{2}-\frac{1}{6}\right)=\frac{3}{4}:\frac{1}{3}=\frac{9}{4}\)

\(\frac{2}{3}.\frac{4}{5}+\frac{1}{3}.\frac{4}{5}=\left(\frac{2}{3}+\frac{1}{3}\right).\frac{4}{5}=1.\frac{4}{5}=\frac{4}{5}\)

\(\frac{1}{2}:\frac{3}{4}+\frac{1}{6}:\frac{3}{4}=\frac{1}{2}.\frac{4}{3}+\frac{1}{6}.\frac{4}{3}=\left(\frac{1}{2}+\frac{1}{6}\right).\frac{4}{3}=\frac{2}{3}.\frac{4}{3}=\frac{8}{9}\)

c,d tương tự 

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)

 1)=133\18

2)=171\5

3)=9\7

4)=431\160

5và 3/8-1 và 5/6

a, 3/4 + 1/4.x=2

    1/4.x        = 2-3/4

     1/4.x      =5/4

     x           = 5/4:1/4

     x           = 5

b, x-2/3.9/4=2,5-1/2

    x-2/3.9/4=2

    x-2/3     =2:9/4

    x-2/3   =8/9

     x        = 8/9+2/3

     x         = 14/9