Nhớ ghi dấu ngoặc tránh giải sai. 

\(a.\)  \(\frac{x+4}{2x+6}+\frac{3}{x^2-9}\)

Ta có: 

\(2x+6=2\left(x+3\right)\)

\(x^2-9=\left(x-3\right)\left(x+3\right)\)

nên \(MTC:\)  \(2\left(x-3\right)\left(x+3\right)\)

Do đó:  \(\frac{x+4}{2x+6}+\frac{3}{x^2-9}=\frac{x+4}{2\left(x+3\right)}+\frac{3}{\left(x-3\right)\left(x+3\right)}=\frac{\left(x+4\right)\left(x-3\right)}{2\left(x-3\right)\left(x+3\right)}+\frac{2.3}{2\left(x-3\right)\left(x+3\right)}=\frac{x^2+x-12+6}{2\left(x-3\right)\left(x+3\right)}\)

\(=\frac{x^2+x-6}{2\left(x-3\right)\left(x+3\right)}=\frac{x^2-2x+3x-6}{2\left(x-3\right)\left(x+3\right)}=\frac{x\left(x-2\right)+3\left(x-2\right)}{2\left(x-3\right)\left(x+3\right)}=\frac{\left(x-2\right)\left(x+3\right)}{2\left(x-3\right)\left(x+3\right)}=\frac{x-2}{2\left(x-3\right)}\)

tick mình đi mình giải cho nha

e) 1/3+1/3:x=1

1/3:x=1-1/3

1/3:x=2/3

x=1/3:2/3

x=1/2

f) x:3/4+1/4=-2/3

x:3/4=-2/3-1/4

x:3/4=-11/12

x=-11/12.3/4

x=-11/16

g) x:(1/2+1/3)=6/5

x:5/6=6/5

x=6/5.5/6

x=1

1/3²<1/2x3

1/4²<1/3x4

.......

1/100²<1/99x100

từ đây => 1/3²+1/4²+....+1/100²<1/2x3+1/3x4+1/4x5+........1/99x100

suy ra..........< 1/2-1/3+1/3-1/4+1/4-1/5................+1/99-1/100

hay............< 1/2 -100

hay........<1/2 vậy 1/3²+1/4²+.....+1/100²<1/2

a) đặt tên biểu thức là A. Ta có :

A =  1.2+2.3+3.4+...+99.100

3A = 1.2.3+2.3.3+3.4.3+...+99.100.3

3A = 1.2.3 + 2.3.(4-1 ) + 3.4.(5-2) + ... + 99.100.(101-98)

3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100

A = 99.100.101 : 3

A = 333300

b) đặt tên biểu thức là B ta có :

B= 1.2+2.3+3.4+...+n.(n+1)

3B = 1.2.3+2.3.3+3.4.3+...+n.(n+1).3

3B = 1.2.3 + 2.3.(4-1) + 3.4.(5-2) + ... + n.(n+1).[ (n+2) - ( n -1 ) ]

3B = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + n.(n+1).(n+2) - (n-1).n.(n+1)

B = n.(n+1).(n+2) : 3

\(A=1\cdot2+2\cdot3+...+99\cdot100\)

\(3\cdot A=1\cdot2\cdot3+2\cdot3\cdot3+...+99\cdot100\cdot3\)

\(3\cdot A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+...+99\cdot100\cdot\left(101-98\right)\)

\(3\cdot A=1\cdot2\cdot3+2\cdot3\cdot4+...+99\cdot100\cdot101-1\cdot2\cdot3-...-98\cdot99\cdot100=\)

\(3\cdot A=99\cdot100\cdot101\)

\(A=99\cdot100\cdot101\div3=333300\)

CCâu b tương tự

1/2 x(1+2) + 1/3 x(1+2+3) + 1/4 x (1+2+3+4) +......+1/16x(1+2+....+16)

=1/2x (2.3/2) + 1/3x( 3.4/2)+....+ 1/16x (16.17/2)

=3/2+4/2+...+17/2

=1/2 (3+4+...+17)

=1/2x 150

=75

nếu còn cách khác thì nhờ bạn giải giùm nha