a, \(\frac{x+1}{2x+6}=\frac{x+1}{2\left(x+3\right)}\)

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

\(=\frac{3x}{2x\left(x+3\right)}-\frac{x-6}{2x\left(x+3\right)}=\frac{2x+6}{2x\left(x+3\right)}=\frac{2\left(x+3\right)}{2x\left(x+3\right)}=\frac{1}{x}\)

c, \(\frac{x-x-2xy+x}{x+2y}+\frac{4xy}{4y^2-x^2}=\frac{x-2xy}{x+2y}+\frac{4xy}{\left(2y-x\right)\left(x+2y\right)}\)

\(=\frac{\left(x-2xy\right)\left(2y-x\right)}{\left(x+2y\right)\left(2y-x\right)}+\frac{4xy}{\left(2y-x\right)\left(x+2y\right)}=\frac{2xy-x^2+4xy^2+2x^2y}{\left(2y-x\right)\left(x+2y\right)}\)

A = x² + x + 1 = ( x² + x + 1/4 ) + 3/4 = ( x + 1/2 )² + 3/4 ≥ 3/4 ∀ x

Dấu "=" xảy ra khi x = -1/2

=> MinA = 3/4 <=> x = -1/2

B = -x² - 4x + 12 = -( x² + 4x + 4 ) + 16 = -( x + 2 )² + 16 ≤ 16 ∀ x

Dấu "=" xảy ra khi x = -2

=> MaxB = 16 <=> x = -2

C = \(\frac{5}{x^2+6}\)

Ta có : x² + 6 ≥ 6 ∀ x

<=> \(\frac{1}{x^2+6}\le\frac{1}{6}\forall x\)

<=> \(\frac{5}{x^2+6}\le\frac{5}{6}\forall x\)

Dấu "=" xảy ra khi x = 0

=> MaxC = 5/6 <=> x = 0

A B C D O E F I

ta có E là trunng điểm AF

      O là trung điểm AC

do đó EO là đường trung bình của tam giác AFC

do đó EO//FC hay tứ giác OEFC là hình thang

b. do OE là đường trung bình nên \(OE=\frac{1}{2}FC=IC\) mà OE //IC nên OEIC là hionhf bình hành 

Đặt \(A=x^2-4x+25=x^2-4x+4+21=\left(x-2\right)^2+21\)

Ta co : \(\left(x-2\right)^2\ge0\forall x;\left(x-2\right)^2+21\ge21\forall x\)

Vậy GTNN A = 21 <=> x = 2 

a,   2x^2 + 3x + 3 2x - 1 x + 2 2x^2 - x 4x + 3 4x - 2 5

b, Để giá trị đa thức A chia hết cho giá trị đa thức B <=> 

\(2x-1\inƯ\left(5\right)=\left\{1;5\right\}\)

a)\(\frac{x^2+xy}{x^2-y^2}=\frac{x\left(x+y\right)}{\left(x-y\right)\left(x+y\right)}=\frac{x}{x-y}\)

b) \(\frac{4}{x+2}+\frac{3}{x-2}+\frac{-5x-2}{x^2-4}\)

\(=\frac{4\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{3\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{-5x-2}{\left(x-2\right)\left(x+2\right)}\)

\(=\frac{4x-8+3x+6-5x-2}{\left(x-2\right)\left(x+2\right)}\)

\(=\frac{2x-4}{\left(x-2\right)\left(x+2\right)}\)

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

a, x(x-y)+2(x-y)=(x-y)(x+2)

b, \(x^2-6xy+9y^2=\left(x-3y\right)^2\)Thay x=16, y=2 có

                \(x^2-6xy+9y^2=\left(x-3y\right)^2=\left(16-2\cdot3\right)^2=10^2=100\)