Algebra Examples

$\frac{5}{4 - \sqrt{3}}$

Step 1

Multiply $\frac{5}{4 - \sqrt{3}}$ by $\frac{4 + \sqrt{3}}{4 + \sqrt{3}}$ .

$\frac{5}{4 - \sqrt{3}} \cdot \frac{4 + \sqrt{3}}{4 + \sqrt{3}}$

Step 2

Multiply $\frac{5}{4 - \sqrt{3}}$ by $\frac{4 + \sqrt{3}}{4 + \sqrt{3}}$ .

$\frac{5 (4 + \sqrt{3})}{(4 - \sqrt{3}) (4 + \sqrt{3})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{5 (4 + \sqrt{3})}{16 + 4 \sqrt{3} - 4 \sqrt{3} - {\sqrt{3}}^{2}}$

Step 4

Simplify.

$\frac{5 (4 + \sqrt{3})}{13}$

Step 5

Since there are no imaginary terms, the complex conjugate is the same as the simplified expression.

$\frac{5 (4 + \sqrt{3})}{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{5 (4 + \sqrt{3})}{13}$

Decimal Form:

$2.20463492 \dots$