Question

Rút gọn

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

B=\(4a+3-\sqrt{\left(2a-1\right)^2}\) với a>\(\dfrac{1}{2}\)

c=\(\dfrac{4}{a^2-4}\sqrt{\left(a-2\right)^2}\) với a<2

Answer 1

`A = sqrt{(a-3)^2 } -3a`

`= |a-3| -3a`

`= 3-a -3a (a<3)`

`=3-4a`

`B= 4a+3 - sqrt{(2a-1)^2} `

`=4a +3 - |2a-1|`

`= 4a +3 -(2a-1)`

`= 4a+3-2a+1 (a>1/2)`

`= 4+2a`

`C=4/(a^2-4) sqrt{(a-2)^2}`

\(=\dfrac{4}{a^2-2^2}\left|a-2\right|=\dfrac{4\left|a-2\right|}{\left(a+2\right)\left(a-2\right)}=\dfrac{4\cdot\left(-1\right)\left(a-2\right)}{\left(a+2\right)\left(a-2\right)}=\dfrac{-4}{a+2}\)`(a<2)`

Answer 2

a: \(A=3-a-3a=3-4a\)

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

c: \(C=\dfrac{4}{\left(a-2\right)\left(a+2\right)}\cdot\left(-1\right)\cdot\left(a-2\right)=-\dfrac{4}{a+2}\)