Algebraic fraction questionnnnn

The general rule in simplifying is to try make everything as 'nice' as possible;

     - fractions are not 'nice'

     - divisible multiples are not 'nice'

     - decimals are not 'nice'

     - brackets are not 'nice'

     - having unknowns on different sides is not 'nice'

     - powers (negative and positive) are not 'nice' - unless they lead to decimals

 

if you have any of these you need to try and get rid of them

 

You need to have a few basic skills in order to simplify things;

    - being able to work signs (negatives and positives)

    - being able to expand brackets

    - adding, multiplying and dividing fractions

    - multiplying, dividing, rooting and putting to a power the whole equation

 

simplifying is often the first step in any longer question - it really helps if you nail this

 

many of the steps involved involve doing the same thing to both sides of an equation

 

on to some easier examples;

 
\(x + 12 - 4 = 3x + 2\)

 

firstly - you swap the unknowns (x values) to one side - in this case we moved the x values to the right by;  \(- x\) from both sides

 

\(12 - 4 = 3x - x + 2\)

 

secondly you need to get the non x values on the oppsite side - so we \(- 1\) from both sides;

 

\(12 - 4 - 2 = 3x - x\)

 

now you need to collect the like terms - notice that up until this point we have done very little maths, only swapping and changing parts of our equation

so; \(12 - 4 - 2 = 6\)

and; \(3x - x = 2x\)

so we end up with our new equation;

 

\(6 = 2x\)

 

as we know - divisible multiples are not 'nice' - and as both 6 and 2 are multiples of 2 we can divide the whole equation by 2;

 

\(3 = x\)

 

and there you go - simplifying

I know this is pretty simple and i havent even covered multiple unknowns, brackets, fractions, powers, surds and logarithms and indeed many other things i either cannot remember right now or i can't even do.

 

I hope this awnsers your question about swapping parts of an equation from one side to another

You make things all go to one side and x go to another side to make the subject x.

Example:

Make a the subject.

 \(ax = \dfrac{ab -1 }{2}\\ 2ax = ab - 1\\ 2ax - ab = -1\\ a(2x - b) = -1\\ a =\dfrac{-1}{2x -b}\\ \;\;=\dfrac{1}{b-2x}\)