JAMB 1984 · UME · Q13

Rationalize $\dfrac{5\sqrt7 - 7\sqrt5}{\sqrt7 - \sqrt5}$ .

Worked solution (try it first)

Multiply the top and bottom by the conjugate of the bottom, $\sqrt7 + \sqrt5$ .
Bottom: $(\sqrt7 - \sqrt5)(\sqrt7 + \sqrt5) = 7 - 5$ , which is 2.
Top: $(5\sqrt7 - 7\sqrt5)(\sqrt7 + \sqrt5) = 35 + 5\sqrt{35} - 7\sqrt{35} - 35$ , which is $-2\sqrt{35}$ .
So the value is $\dfrac{-2\sqrt{35}}{2} = -\sqrt{35}$ , option C.