(a+b).(a+b)=(a+b)²

(a+b)(a+b)=(a+b)^2

\(\left(a+b\right)\left(a+b\right)\)

\(=\left(a+b\right)^2\)

\(=a^2+2ab+b^2\)

\(\sqrt{\frac{a}{b}}+\sqrt{ab}+\frac{a}{b}\sqrt{\frac{b}{a}}\)

\(=\sqrt{\frac{a}{b}}+\sqrt{ab}+\sqrt{\frac{a^2b}{b^2a}}\)

\(=\sqrt{\frac{a}{b}}+\sqrt{ab}+\sqrt{\frac{a}{b}}\)

\(=2\sqrt{\frac{a}{b}}+\sqrt{ab}\)

= ( -a ) -b +c + a +b +c

=[ ( -a ) + a ] + b - b + c + c

= 0 + ( b-b ) + ( c+c )

=0+0+  2x

=2x

(-a-b+c)-(-a-b-c)=-a-b+c+a+b+c=2c

(-a-b+c) - (-a-b-c)

=-a-b+c+a+b+c

=(a-a)+(b-b)+(c+c)

=0+0+c.2

=c2

A = (-a - b + c) - (-a - b - c)

= -a - b + c + a + b + c

= (a - a) + (b - b) + (c + c)

= 0 + 0 + 2c

= 2c

A = (-a - b + c ) - ( -a - b - c )

A = -a -b - c + a + b + c

A = (-a + a ) + (-b + b ) + (c + c)

A= 0 + 0 + 2c

A= 2c

Vay A= 2c

tik nha

A = (-a-b+c)-(-a-b-c)

   = -a-b+c+a+b+c

   = (-a+a)-(b-b)+(c+c)

   = 0-0+c.2

   = c.2

= -a - b + c + a + b +c -2b

= 2c- 2b

=2. ( c - b)

hok tốt

\(\left(-a-b+c\right)-\left(-a-b-c\right)-2b\)

\(=-a-b+c+a+b+c-2b\)

\(=2c-2b=2.\left(c-b\right)\)

 =   -a - b + c +a + b + c -2b

= 2c - 2b

= 2.(c - b)

hok tốt

=-a    -    b    +    c     +    a    +    b   +    c   -     2b

=2c    -    2b

=2    .     (   c   -   b)

học tốt nha bạn hiền

Dùng hằng đẳng thức A² + 2AB + B² = ( A + B)² :

Ta được ... = (a-b+c+b-c)² = a²

a:

ĐKXĐ: x<>2

|2x-3|=1

=>\(\left[{}\begin{matrix}2x-3=1\\2x-3=-1\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=2\left(loại\right)\\x=1\left(nhận\right)\end{matrix}\right.\)

Thay x=1 vào A, ta được:

\(A=\dfrac{1+1^2}{2-1}=\dfrac{2}{1}=2\)

b: ĐKXĐ: \(x\notin\left\{-1;2\right\}\)

\(B=\dfrac{2x}{x+1}+\dfrac{3}{x-2}-\dfrac{2x^2+1}{x^2-x-2}\)

\(=\dfrac{2x}{x+1}+\dfrac{3}{x-2}-\dfrac{2x^2+1}{\left(x-2\right)\left(x+1\right)}\)

\(=\dfrac{2x\left(x-2\right)+3\left(x+1\right)-2x^2-1}{\left(x+1\right)\left(x-2\right)}\)

\(=\dfrac{2x^2-4x+3x+3-2x^2-1}{\left(x+1\right)\left(x-2\right)}\)

\(=\dfrac{-x+2}{\left(x+1\right)\left(x-2\right)}=-\dfrac{1}{x+1}\)

c: \(P=A\cdot B=\dfrac{-1}{x+1}\cdot\dfrac{x\left(x+1\right)}{2-x}=\dfrac{x}{x-2}\)

\(=\dfrac{x-2+2}{x-2}=1+\dfrac{2}{x-2}\)

Để P lớn nhất thì \(\dfrac{2}{x-2}\) max

=>x-2=1

=>x=3(nhận)