Question

How would the fraction 7}{1-\sqrt{5} }" alt="\frac{7}{1-\sqrt{5} }" align="absmiddle" class="latex-formula"> be rewritten if its denominator is rationalized using difference of squares?

Answer 1

Answer:

$\frac{7 + 7 \sqrt{5} }{ - 4}$

Step-by-step explanation:

We would multiply the fraction by its conjugate

( A conjugate is a expression that has the same integer or number values but have different signs) for example

$5x + 2$

and

$5x - 2$

ARE Conjugates.

The conjugate of

$1 - \sqrt{5}$

is

$1 + \sqrt{5}$

So this means we will multiply the expression by 1 plus sqr root of 5 on the numerator and denominator.

Our new numerator will be

$7 \times (1 + \sqrt{5} ) = 7 + 7 \sqrt{5}$

We can apply the difference of squares for the denominator.

$(x + y)(x - y) = x {}^{2} - {y}^{2}$

So our denominator will be

$1 - 5 = - 4$

So our rationalized fraction will be

$\frac{7 + 7 \sqrt{5} }{ - 4}$