GCSE revision notes

Solving equations where the DENOMINATOR has an algebraic term

To solve an equation such as:

 

We multiply by . This has the effect of cancelling the  on the left hand side whilst introducing it at the top on the other side.

 

So we get:

 

 

Or

 

 

Suppose instead our equation is:

 

Multiply by

 

                                                                

Or

 

Solve:

 

Imagine this as:

So,

Expand,

 

Rewrite,

 

 Solve:

Expand,

So,

Expand again

Rewrite,

 

 

 

 

 

 

What if there are more terms to deal with in the equation?

Example 1:

Solve:

 

 

 

 

 

 

Example 3:

Solve:

 

 

This is the same as:

 

Make all terms have the same denominator, this requires some thought

The lowest common multiple of  

So the lowest common multiple of

 

 

 

 

So the equation becomes:

Or,

Rewrite,

 

 

 

Example 2:

Write as:

Look for lowest common multiple of all the denominators, which is 4,  and convert each of the denominators to 4

 

 

 

Cancel the denominator: