Thread: Algebra

Ok any ideas on a quick way of cancelling expressions like this?

$\displaystyle
\frac{{2\sqrt {5x - 1} - \frac{{5(2x + 7)}}
{{2\sqrt {5x - 1} }}}}
{{(5x - 1)}}
$

I'm just getting a bit lost..

Multiply the expression by $\displaystyle \frac{\sqrt{5x-1}}{\sqrt{5x-1}}$. See where that gets you

This right..?

$\displaystyle
\frac{{\frac{{2\sqrt {5x - 1} }}
{1} - \frac{{5(2x + 7)}}
{{2\sqrt {5x - 1} }}}}
{{(5x - 1)}}
$

$\displaystyle
\begin{gathered}
\frac{{\frac{{2\sqrt {5x - 1} (2\sqrt {5x - 1} )}}
{{2\sqrt {5x - 1} }} - \frac{{(1)5(2x + 7)}}
{{2\sqrt {5x - 1} }}}}
{{(5x - 1)}} \hfill \\
\hfill \\
\frac{{\frac{{5x - 20 - 7x + 7 - 10x - 7}}
{{2\sqrt {5x - 1} }}}}
{{5x - 1}} \hfill \\
\end{gathered}
$

$\displaystyle
\frac{{\frac{{ - 12x - 20}}
{{2\sqrt {5x - 1} }}}}
{{5x - 1}}
$

Also at this stage I have read conflicting Ideas...

Is a/b/c = c * a / b
OR
a/b/c = a / b*c

How do you know which one to choose..??

.......

Can anyone help?..