Q. 8.105 - Intermediate Algebra

Question

In the following exercise ,simplify 

$\frac{3}{1-\sqrt{5}}$

Step-by-Step Solution

Answer

$\frac{-3(\sqrt{5}+1)}{4}$ .

Part (a) Step 1. Given information.

Given expression:

$\frac{3}{1-\sqrt{5}}$

Part (a) Step 2. Finding solution.

Finding the solution.

Multiply numerator and denominator by the same factor i.e conjugate of denominator.

Multiply numerator and denominator $1+\sqrt{5}$.

$$\begin{gathered} \frac{3}{1-\sqrt{5}}\times \frac{1+\sqrt{5}}{1+\sqrt{5}} \\ =\frac{3(1+\sqrt{5})}{{\left(1\right)}^2-(\sqrt{5{)}^2}} \\ =\frac{3(1+\sqrt{5})}{1-5} \\ =\frac{-3(1+\sqrt{5)}}{4} \end{gathered}$$