# Simple algebra question.

• Sep 20th 2009, 06:20 AM
Splint
Simple algebra question.
Please be understanding if this is a stupid question as I am making a comeback to algebra after 20 years of not using it.

The following appears in my text book...
$\displaystyle \frac{x}{3\sqrt(100^2+x^2)}=\frac{1}{5}$
the next line is....
$\displaystyle 5x=3\sqrt(100^2+x^2)$
it is the $\displaystyle 5x$ which bothers me, I would have thought to multiply both sides by $\displaystyle 3\sqrt(100^2+x^2)$ then divide both sides by $\displaystyle \frac{1}{5}$ which would in my mind result in $\displaystyle \frac{x}{5}=3\sqrt(100^2+x^2)$
Have I missed the point here?

Splint
• Sep 20th 2009, 06:34 AM
aidan
Quote:

Originally Posted by Splint
Please be understanding if this is a stupid question as I am making a comeback to algebra after 20 years of not using it.

The following appears in my text book...
$\displaystyle \frac{x}{3\sqrt(100^2+x^2)}=\frac{1}{5}$
the next line is....
$\displaystyle 5x=3\sqrt(100^2+x^2)$
it is the $\displaystyle 5x$ which bothers me, I would have thought to multiply both sides by $\displaystyle 3\sqrt(100^2+x^2)$ then divide both sides by $\displaystyle \frac{1}{5}$ which would in my mind result in $\displaystyle \frac{x}{5}=3\sqrt(100^2+x^2)$
Have I missed the point here?

Splint

Division by $\displaystyle \dfrac{1}{5}$ is equivalent to multiplication by 5.
You have divided the RHS by $\displaystyle \dfrac{1}{5}$,
but
you have divided the LHS by 5.

You multiplied through with the square root part and had no problem -- follow that by multiply both sides by 5.