\(\frac{2}{x.\left(x+2\right)}+\frac{2}{3.5}+\frac{2}{5.7}.+.....+\frac{2}{99.101}=\frac{100}{101}\)

\(\Rightarrow\frac{1}{x\left(x+1\right)}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{99.101}=\frac{100}{101}\)

\(\Rightarrow\frac{1}{x}-\frac{1}{x+1}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{99}-\frac{1}{101}=\frac{100}{101}\)

\(\Rightarrow\frac{1}{x}-\frac{1}{101}=\frac{100}{101}\)

\(\Rightarrow\frac{1}{x}=\frac{101}{101}\)

\(\Rightarrow\frac{1}{x}=\frac{1}{1}\)

\(\Rightarrow x=1\)

Phân phối:

= ( 145 x 99 + 145 x 1 ) - ( 143 x 101 - 143 x 1 )

= 145 x (99 + 1) - [143 x (101 - 1)]
= 145 x 100 - 143 x 100
= (145 - 143) x 100
= 2 x 100 = 200

=2323

x + 99 = 99 + 100 + 101

x + 99 = 199 + 101

x + 99 = 300

x = 300 - 99

x = 201.

x = 201 

kick mình nha

Xét 99 x 101

= ( 100 - 1 ) x ( 101 - 1 )

= 100 x 100 + 1 x 101 - 1 x 101 - 1 x 1 

= 100 x 100 - 1

Vậy 99 x 101 < 100 x 100

nhầm chút 

Xét 99 x 101

= ( 100 - 1 ) x ( 100 + 1 )

= 100 x 100 + 1 x 101 - 1 x 101 - 1 x 1 

= 100 x 100 - 1

Vậy 99 x 101 < 100 x 100

=145x(99+1)-143x(101-1)

=145x100 - 143x100

=100x(145-143)

=100x2

=200

Ta có: \(\left(145\times99+145\right)-\left(143\times101-143\right)\)

\(=145\times\left(99+1\right)-143\times\left(101-1\right)\)

\(=145\times100-143\times100=100\times2\)

Ta có: \(4\times113\times25-5\times112\times20\)

\(=100\times113-100\times112\)

\(=100\times\left(113-112\right)=100\times1=100\)

Ta có: \(\frac{\left(145\times99+145\right)-\left(143\times101-143\right)}{4\times113\times25-5\times112\times20}\)

\(=\frac{100\times2}{100}=2\)