i have 2 more question that i tried to do but not sure do i have to go further. Thanks.
Link to problem.
ImageShack - Hosting :: 36817195gr4.png
i have 2 more question that i tried to do but not sure do i have to go further. Thanks.
Link to problem.
ImageShack - Hosting :: 36817195gr4.png
For the first one, you forgot $\displaystyle \sqrt{a-b}$ in the numerator again !
$\displaystyle \frac{\sqrt{a-b}\sqrt{a+b}}{a-b}=\frac{\sqrt{(a-b)(a+b)}}{a-b}=\frac{\sqrt{a^2-b^2}}{a-b}$
For the second one, assume that x,y>0 :
$\displaystyle \frac{\sqrt{x^3 y^5}}{x^3y^5}=\frac{\sqrt{x^2 y^4 xy}}{x^3y^5}=\frac{xy^2 \sqrt{xy}}{x^3y^5}=\dots$
$\displaystyle \frac{{\sqrt {a + b} }}
{{\sqrt {a - b} }} \hfill \\$
$\displaystyle = \frac{{\sqrt {a + b} }}
{{\sqrt {a - b} }} \times \frac{{\sqrt {a - b} }}
{{\sqrt {a - b} }} \hfill \\$
$\displaystyle = \frac{{\sqrt {\left( {a + b} \right)\left( {a - b} \right)} }}
{{a - b}} \hfill \\$
$\displaystyle = \frac{{\sqrt {a^2 - b^2 } }}
{{a - b}} \hfill \\
\hfill \\$
$\displaystyle {\text{Now, for second question}}{\text{.}} \hfill \\$
$\displaystyle \frac{1}
{{\sqrt {x^3 y^5 } }} = \frac{1}
{{\sqrt {x^2 xy^4 y} }} = \frac{1}
{{xy^2 \sqrt {xy} }} \hfill \\$
$\displaystyle = \frac{1}
{{xy^2 \sqrt {xy} }} \times \frac{{\sqrt {xy} }}
{{\sqrt {xy} }} \hfill \\$
$\displaystyle = \frac{{\sqrt {xy} }}
{{xy^2 xy}} = \frac{{\sqrt {xy} }}
{{x^2 y^3 }} \hfill \\
$