Secondary V • 10mo.
Hello. I need help with a math question. I need to rationalize and simplify it.
(SquareRoot(4+h) - 2) / h
Hello. I need help with a math question. I need to rationalize and simplify it.
(SquareRoot(4+h) - 2) / h
Explanation from Alloprof
This Explanation was submitted by a member of the Alloprof team.
Hello,
The concept sheet called Rationalizing Fractions tells you the method to apply.
You have to identify the numerator's conjugate, meaning the same expression but with the opposite operation.
For (SquareRoot(4+h) - 2), the conjugate is (SquareRoot(4+h) + 2).
Thus, you will have the following calculations.
$$ \begin{align} \frac{\sqrt{4+h}-2}{h}&=\frac{\sqrt{4+h}-2}{h}\cdot\frac{\sqrt{4+h}+2}{\sqrt{4+h}+2}\\ &=\frac{(4+h)-4}{h(\sqrt{4+h}+2)}\\ &=\frac{h}{h(\sqrt{4+h}+2)}\\ &=\frac{1}{\sqrt{4+h}+2}\\ \end{align} $$
Do not hesitate if you have more questions!