1. ## Engineering Maths help

I am having a blond moment. Cant see how this is done but I know it is simple, Can someone explain please.
I have a revision Question at Uni. part of it says Multiply the top and Botom of the equation by 1+4s but i cant see how it works. please see the attachment

2. Originally Posted by bobbych
I am having a blond moment. Cant see how this is done but I know it is simple, Can someone explain please.
I have a revision Question at Uni. part of it says Multiply the top and Botom of the equation by 1+4s but i cant see how it works. please see the attachment

the fact that $\displaystyle \frac{a}{b}=\frac{ax}{bx}$ if $\displaystyle b,x \neq 0$ has been used.

3. So here's what yo have:

$\displaystyle \frac{\frac{6}{1 + 4s}}{1 + (\frac{6}{1 + 4s})3} = \frac{\frac{6}{1 + 4s}}{1 + \frac{18}{1 + 4s}}$

If simplifying is what you are trying to do, then yes you can multiply the top and bottom by $\displaystyle 1 + 4s$ will help.

What you have in your attachment is:

$\displaystyle \frac{6}{1 + 4s + 18} = \frac{6}{4s + 19}$

Although this is a true statement, I don't think you did it right.

I think the numerator is correct, but when you multiply the denominator by $\displaystyle 1 + 4s$ it needs to look like:

$\displaystyle ((1 + (\frac{6}{1 + 4s})3)(1 + 4s)$

In other words you need to multiply it like
$\displaystyle (a + b)(c + d) = ac + ad + bc + bd$

So try this out and see what you get; hope this helps.

4. When dealing with fractions, it's nearly always best to have a common denominator. This is even more true when you have fractions of fractions.

You have \displaystyle \displaystyle \begin{align*}\frac{\frac{6}{1 + 4s}}{1 + \frac{18}{1 + 4s}} &= \frac{\frac{6}{1 + 4s}}{\frac{1 + 4s + 18}{1 + 4s}}\\ &= \frac{\frac{6}{1 + 4s}}{\frac{19 + 4s}{1 + 4s}} \\ &= \frac{6}{1 + 4s} \cdot \frac{1 + 4s}{19 + 4s} \\ &= \frac{6}{19 + 4s}\end{align*}