Question

Thực hiện phép tính:

a, x+1/2x+6 + 2x+3/x²+3x

b, 3/2x+6 - x-6/2x+6x

c, x/x-2y + x/x+2y + 4xy/4y²-x²

d, 1/3x-2 - 1/3x+2 - 3x-6/4-9x²

Phân tích đa thức thành nhân tử:

a²-b²-4ab+4

Answer 1

a)\(\dfrac{x+1}{2x+6}\)+\(\dfrac{2x+3}{x^2+3x}\)

\(2x+6=2\left(x+3\right)\)

\(x^2+3x=x\left(x+3\right)\)

MC:\(2x\left(x+3\right)\)

\(\dfrac{x^2+x}{2x\left(x+3\right)}\)+\(\dfrac{2\times\left(2x+3\right)}{2x\left(x+3\right)}\)=0

\(\Leftrightarrow x^2+x+4x+6\)=0

\(\Leftrightarrow x^2+5x+6\)=0

\(\Leftrightarrow x^2+2x+3x+6\)=0

\(\Leftrightarrow\left(x^2+2x\right)+\left(3x+6\right)\)=0

\(\Leftrightarrow x\left(x+2\right)+3\left(x+2\right)\)=0

\(\Leftrightarrow\left(x+2\right)\left(x+3\right)=0\)

\(\Leftrightarrow x+2=0\) hoặc \(x+3=0\)

\(\Leftrightarrow x+2=0\Rightarrow x=-2\)

\(\Leftrightarrow x+3=0\Rightarrow x=-3\)

S={-2;-3}