Ngoặc thứ nhất dấu giữa 2 phân số là gì vậy bạn?

\(A=\left|a-3\right|-3a=3-a-3a=3-4a\)

\(B=4a+3-\left|2a-1\right|=4a+3-2a+1=2a+4\)

\(C=\dfrac{4}{a^2-4}\left|a-2\right|=\dfrac{-4\left(a-2\right)}{\left(a-2\right)\left(a+2\right)}=\dfrac{-4}{a+2}\)

\(D=\dfrac{a^2-9}{12}:\sqrt{\dfrac{\left(a+3\right)^2}{16}}=\dfrac{a^2-9}{12}:\dfrac{\left|a+3\right|}{4}=\dfrac{\left(a-3\right)\left(a+3\right).4}{-12\left(a+3\right)}=\dfrac{3-a}{3}\)

\(A=\sqrt{\left(a-3\right)^2}-3a\)

=3-a-3a

=3-4a

a)

Để B được xác định khi:

*\(2a^2+6a\ne0\Rightarrow2a\left(a+3\right)\ne0\)

=>\(a\ne0\) và \(a+3\ne0\Rightarrow a\ne-3\)

*a²-9\(\ne\)0

=>(a+9)(a-9)\(\ne\)0

=> a+9\(\ne\)0 và a-9\(\ne\)0

=> a \(\ne\)-9 và a\(\ne\)9

Vậy để B được xác định khi a\(\in\){-9;-3;0;9}

b)

\(\dfrac{\left(a+3\right)^2}{2a^2+6a}\cdot\left(1-\dfrac{6a-18}{a^2-9}\right)\)

=\(\dfrac{\left(a+3\right)^2}{2a\left(a+3\right)}.\left(1-\dfrac{6\left(a-3\right)}{\left(a-3\right)\left(a+3\right)}\right)\)

=\(\dfrac{a+3}{2a}\cdot\left(1-\dfrac{6}{a+3}\right)\)

=\(\dfrac{a+3}{2a}\cdot\left(\dfrac{a+3-6}{a+3}\right)\)

=\(\dfrac{a+3}{2a}\dfrac{a-3}{a+3}\)

=\(\dfrac{a-3}{2a}\)

c) Ta có B=0

=>\(\dfrac{a-3}{2a}=0\\ \Rightarrow a-3=0\\ \Rightarrow a=3\)

Vậy B=0 khi a=3

d)Ta có B=1

\(\Rightarrow\dfrac{a-3}{2a}=1\\ \Rightarrow a-3=2a\\ \Rightarrow a-2a=3\\ \Rightarrow-a=3\\ \Rightarrow a=-3\left(KTMDK\right)\)

a)

Để B được xác định khi:

*$2a^2+6a\ne 0\Rightarrow 2a\left(a+3\right)\ne 0$

=>$a\ne 0$ và $a+3\ne 0\Rightarrow a\ne -3$

*a2-9$\ne$0

=>(a+9)(a-9)$\ne$0

=> a+9$\ne$0 và a-9$\ne$0

=> a $\ne$-9 và a$\ne$9

Vậy để B được xác định khi a$\in${-9;-3;0;9}

b)

$\frac{{\left(a+3\right)}^2}{2a^2+6a}\cdot \left(1-\frac{6a-18}{a^2-9}\right)$

=$\frac{{\left(a+3\right)}^2}{2a\left(a+3\right)}.\left(1-\frac{6\left(a-3\right)}{\left(a-3\right)\left(a+3\right)}\right)$

=$\frac{a+3}{2a}\cdot \left(1-\frac{6}{a+3}\right)$

=$\frac{a+3}{2a}\cdot \left(\frac{a+3-6}{a+3}\right)$

=$\frac{a+3}{2a}\frac{a-3}{a+3}$

=$\frac{a-3}{2a}$

c) Ta có B=0

=>$\frac{a-3}{2a}=0\Rightarrow a-3=0\Rightarrow a=3$

Vậy B=0 khi a=3

d)Ta có B=1

$\Rightarrow \frac{a-3}{2a}=1$

\(-\left(\dfrac{a-1}{a+1}-\dfrac{a}{a-1}-\dfrac{3a+1}{1-a^2}\right):\dfrac{2a+1}{a^2-1}\left(dk:a\ne1,a\ne-1\right)\)

\(=-\left(\dfrac{a-1}{a+1}-\dfrac{a}{a-1}+\dfrac{3a+1}{a^2-1}\right):\dfrac{2a+1}{\left(a-1\right)\left(a+1\right)}\\ =-\left(\dfrac{\left(a-1\right)^2-a\left(a+1\right)+3a+1}{\left(a-1\right)\left(a+1\right)}\right).\dfrac{\left(a-1\right)\left(a+1\right)}{2a+1}\\ =-\dfrac{a^2-2a+1-a^2-a+3a+1}{\left(a-1\right)\left(a+1\right)}.\dfrac{\left(a-1\right)\left(a+1\right)}{2a+1}\)

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

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

__

\(-\dfrac{2}{2a+1}=\dfrac{3}{a-1}\\ \Leftrightarrow-2\left(a-1\right)=3\left(2a+1\right)\\ \Leftrightarrow-2a+2-6a-3=0\\ \Leftrightarrow-8a-1=0\\ \Leftrightarrow-8a=1\\ \Leftrightarrow a=-\dfrac{1}{8}\)

a) \(P=\dfrac{\sqrt{a}\left[\left(\sqrt{a}\right)^3+1\right]}{a-\sqrt{a}+1}-\dfrac{\sqrt{a}\left(2\sqrt{a}+1\right)}{\sqrt{a}}+1\)

\(P=\dfrac{\sqrt{a}\left(\sqrt{a}+1\right)\left(a-\sqrt{a}+1\right)}{a-\sqrt{a}+1}-\left(2\sqrt{a}+1\right)+1\)

\(P=\sqrt{a}\left(\sqrt{a}+1\right)-\left(2\sqrt{a}+1\right)+1\)

\(P=a+\sqrt{a}-2\sqrt{a}-1+1\)

\(P=a-\sqrt{a}\)

b) Với a > 1 thì \(a>\sqrt{a}\) , do đó \(P=a-\sqrt{a}>0\), suy ra \(\left|P\right|=P\)

c) \(A=a-\sqrt{a}=\left(\sqrt{a}-\dfrac{1}{2}\right)^2-\dfrac{1}{4}\ge-\dfrac{1}{4}\)

Vậy A nhỏ nhất bằng \(-\dfrac{1}{4}\) khi cà chỉ khi \(\sqrt{a}=\dfrac{1}{2}\) hay \(a=\dfrac{1}{4}\)

a: \(P=\sqrt{a}\left(\sqrt{a}+1\right)-2\sqrt{a}-1+1=a-\sqrt{a}\)

b: a>1 nên P>0

\(\Leftrightarrow P=\left|P\right|\)