Question

Cho biểu thức P=\(\dfrac{2a^2+4}{1-a^3}-\dfrac{1}{1+\sqrt{a}}-\dfrac{1}{1-\sqrt{a}}\)

Tìm điều kiện của a để P xác định

Rút gọn biểu thức P

Answer 1

\(P=\dfrac{2a^2+4}{1-a^3}-\dfrac{1}{1+\sqrt{a}}-\dfrac{1}{1-\sqrt{a}}\\ =\dfrac{2a^2+4}{\left(1-a\right)\left(1+a+a^2\right)}-\dfrac{1}{1+\sqrt{a}}-\dfrac{1}{1-\sqrt{a}}\\ =\dfrac{2a^2+4-\left(1-\sqrt{a}\right)\left(1+a+a^2\right)-\left(1+\sqrt{a}\right)\left(1+a+a^2\right)}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)\left(1+a+a^2\right)}\\ =\dfrac{2-2a}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)\left(1+a+a^2\right)}\\ =\dfrac{2\left(1-a\right)}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)\left(1+a+a^2\right)}\\ =\dfrac{2\left(1-a\right)}{\left(1-a\right)\left(1+a+a^2\right)}\\ =\dfrac{2}{1+a+a^2}\)