Question

[22 - Đỗ Nhật Minh - 6A17]

Answer 1

[Nguyễn Lê Phước Thịnh]

a: \(3x\left(x-2\right)=x^2-4\)

=>\(3x\left(x-2\right)-\left(x-2\right)\left(x+2\right)=0\)

=>\(\left(x-2\right)\left(3x-x-2\right)=0\)

=>(x-2)(2x-2)=0

=>2(x-2)(x-1)=0

=>(x-1)(x-2)=0

=>\(\left[{}\begin{matrix}x-1=0\\x-2=0\end{matrix}\right.\)

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

b:

ĐKXĐ: \(x\notin\left\{1;-1\right\}\)

 \(\dfrac{x+3}{x-1}+\dfrac{x}{x+1}=\dfrac{x^2+4x+5}{x^2-1}\)

=>\(\dfrac{\left(x+3\right)\left(x+1\right)+x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{x^2+4x+5}{\left(x-1\right)\left(x+1\right)}\)

=>\(\left(x+3\right)\left(x+1\right)+x\left(x-1\right)=x^2+4x+5\)

=>\(x^2+4x+3+x^2-x-x^2-4x-5=0\)

=>\(x^2-x-2=0\)

=>(x-2)(x+1)=0

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

c: \(3\left(x-1\right)< 5\left(x+1\right)-2\)

=>\(3x-3< 5x+5-2\)

=>3x-3<5x+3

=>-2x<6

=>x>-3

d: \(x^3>-2x\)

=>\(x^3+2x>0\)

=>\(x\left(x^2+2\right)>0\)

mà \(x^2+2>0\forall x\)

nên x>0