Question

Answer 1

6) \(\dfrac{2x}{4+\sqrt{x}}\)

\(=\dfrac{2x\left(4-\sqrt{x}\right)}{\left(4+\sqrt{x}\right)\left(4-\sqrt{x}\right)}\)

\(=\dfrac{8x-2x\sqrt{x}}{4^2-\left(\sqrt{x}\right)^2}\)

\(=\dfrac{8x-2x\sqrt{x}}{16-x}\)

Answer 2

6) \(\dfrac{2x}{4+\sqrt{x}}=\dfrac{2\sqrt{x}\left(\sqrt{x}+4\right)-(8\sqrt{x}+32)+32}{\sqrt{x}+4}\)

\(=\dfrac{\left(2\sqrt{x}-8\right)\left(\sqrt{x}+4\right)+32}{\sqrt{x}+4}\)

\(=2\sqrt{x}-8+\dfrac{32}{\sqrt{x}+4}\)