Question

cho bieetr thức M= 6x+ \(\left(\dfrac{x}{x-2}-\dfrac{x}{x+2}\right):\dfrac{4x}{x^4-2x^3+8x-16}\)

a, rút gọn M

b, tìm x sao cho M²=M
c, tìm x sao cho M²>M

Answer 1

a: \(M=6x+\dfrac{x^2+2x-x^2+2x}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{\left(x^2-4\right)\left(x^2+4\right)-2x\left(x^2-4\right)}{4x}\)

\(=6+\dfrac{4x}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{\left(x^2-4\right)\left(x^2-2x+4\right)}{4x}\)

\(=6+x^2-2x+4=x^2-2x+10\)

b: Để \(M^2=M\) thì M=0 hoặc M=1

=>\(x\in\varnothing\)

c: Vì \(M=x^2-2x+10=\left(x-1\right)^2+9>0\)

nên \(M^2>M\forall x\)