Question

Answer 1

a: \(A=\left(1+\dfrac{\sqrt{a}\left(1+\sqrt{a}\right)}{1+\sqrt{a}}\right)\left(1-\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)\)

=(1+căn a)(1-căn a)

=1-a

c: \(C=\left(\dfrac{1}{2+2\sqrt{x}}+\dfrac{1}{2-2\sqrt{x}}-\dfrac{x+1}{1-x^2}\right)\left(1-\dfrac{1}{x}\right)\)

\(=\left(\dfrac{1}{2\left(\sqrt{x}+1\right)}-\dfrac{1}{2\left(\sqrt{x}-1\right)}+\dfrac{1}{x-1}\right)\cdot\dfrac{x-1}{x}\)

\(=\dfrac{\sqrt{x}-1-\sqrt{x}-1+2}{2\left(x-1\right)}\cdot\dfrac{x-1}{x}=0\)