Question

[Mai Anh]

Tính

\(\dfrac{3}{x^2+6x+9_{ }}+\dfrac{2}{6x-x-9}+\dfrac{x^2+30x-27}{x^4-18x^2+81}\)

Answer 1

[Mai Anh]

Akai Haruma Nguyễn Huy Tú Nguyễn Huy ThắngHồng Phúc NguyễnPhạm Hoàng Giang......và nhiều bạn nữa giúp mik vs

Answer 2

[lê thị hương giang]

\(\dfrac{3}{x^2+6x+9}+\dfrac{2}{6x-x^2-9}+\dfrac{x^2+30x-27}{x^4-18x^2+81}\)

\(=\dfrac{3}{\left(x+3\right)^2}+\dfrac{-2}{\left(x-3\right)^2}+\dfrac{x^2+30x-27}{x^4-9x^2-9x^2+81}\)

\(=\dfrac{3}{\left(x+3\right)^2}-\dfrac{2}{\left(x-3\right)^2}+\dfrac{x^2+30x-27}{\left(x-3\right)^2\left(x+3\right)^2}\)

\(=\dfrac{3\left(x-3\right)^2}{\left(x+3\right)^2\left(x-3\right)^2}-\dfrac{2\left(x+3\right)^2}{\left(x+3\right)^2\left(x-3\right)^2}+\dfrac{x^2+30x-27}{\left(x-3\right)^2\left(x+3\right)^2}\)

\(=\dfrac{3x^2-18x+27-2x^2-12x-18+x^2+30x-27}{\left(x-3\right)^2\left(x+3\right)^2}\)

\(=\dfrac{2x^2-18}{\left(x-3\right)^2\left(x+3\right)^2}\)

\(=\dfrac{2\left(x^2-9\right)}{\left(x-3\right)^2\left(x+3\right)^2}\)

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

\(=\dfrac{2}{\left(x-3\right)\left(x+3\right)}=\dfrac{2}{x^2-9}\)