Question

Cho P = \(\dfrac{\sqrt{a}+3}{\sqrt{a}-2}-\dfrac{\sqrt{a-1}}{\sqrt{a}+2}+\dfrac{4\sqrt{a}-4}{4-a}\) (a>0; a≠4)

a) Rút gọn P

b) tính giá tri của P với a=9

Answer 1

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

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

⇒ P = \(\sqrt{a^2}+2\sqrt{a}+3\sqrt{a}+6-\sqrt{a^2}-2\sqrt{a}-\sqrt{a}+2+4\sqrt{a}-4\)

P = \(4+6\sqrt{a}\)

b) Ta thay a = 9 vào P = \(4+6\sqrt{a}\)

P = \(4+6\sqrt{9}\) = \(4+6\sqrt{9}\) = \(4+6.3\) = \(22\)