Question

Giúp mình bài 19 với ạ!!!

Answer 1

19:

a: ĐKXĐ: \(x\notin\left\{10;-10;\sqrt{10};-\sqrt{10}\right\}\)

b: \(P=\left(\dfrac{5x+2}{x^2-10}+\dfrac{5x-2}{x^2+10}\right)\cdot\dfrac{x^2-100}{x^2+4}\)

\(=\dfrac{\left(5x+2\right)\left(x^2+10\right)+\left(5x-2\right)\left(x^2-10\right)}{\left(x^2-10\right)\left(x^2+10\right)}\cdot\dfrac{x^2-100}{x^2+4}\)

\(=\dfrac{5x^3+50x+2x^2+20+5x^3-50x-2x^2+20}{\left(x^2-10\right)\left(x^2+10\right)}\cdot\dfrac{x^2-100}{x^2+4}\)

\(=\dfrac{10x^3+40}{x^4-100}\cdot\dfrac{x^2-100}{x^2+4}\)

\(=\dfrac{\left(10x^3+40\right)\left(x^2-100\right)}{\left(x^4-100\right)\cdot\left(x^2+4\right)}\)