Question

Cho biểu thức : \(\frac{3}{x+5}+\frac{2}{x-5}-\frac{2x+10}{\left(x+5\right)\left(x-5\right)}\)

a) Rút gọn

b) Tìm x ∈ Z để E ∈ Z

Answer 1

\(a)\dfrac{3}{{x + 5}} + \dfrac{2}{{x - 5}} - \dfrac{{2x + 10}}{{\left( {x + 5} \right)\left( {x - 5} \right)}} = \dfrac{3}{{x + 5}} + \dfrac{2}{{x - 5}} - \dfrac{{2x + 10}}{{\left( {x + 5} \right)\left( {x - 5} \right)}}\\ = \dfrac{3}{{x + 5}} + \dfrac{2}{{x - 5}} - \dfrac{{2\left( {x + 5} \right)}}{{\left( {x + 5} \right)\left( {x - 5} \right)}}\\ = \dfrac{3}{{x + 5}} + \dfrac{2}{{x - 5}} - \dfrac{2}{{x - 5}}\\ = \dfrac{3}{{x + 5}}\\ \)