# Checking for careless mistakes using the Substitution Method

• Normal method of checking (i.e. check your working from front to back again), may or may not find the error
• Using Substitution Method of checking guarantees that your answer is correct, and will find an error if there is one.
• Use  Substitution Method of checking for all algebra/solving/simplify questions worth 2 marks or more. You will be able to save many many marks using this method!
• Only takes 10 seconds with practice. (use calculator)

### Example (using substitution method)

Express $\displaystyle\frac{2x-3}{x^2+4x+3}-\frac{1}{x+3}$ as a single fraction in its simplest form. [2 marks]

After getting your answer ($\displaystyle\frac{x-4}{(x+3)(x+1)}$), you can substitute in the value $\boxed{x=9}$.

When, $x=9$, $\displaystyle\frac{2x-3}{x^2+4x+3}-\frac{1}{x+3}=\frac{1}{24}$, and $\displaystyle\frac{x-4}{(x+3)(x+1)}=\frac{1}{24}$

Since both expressions give the same value, you have just checked that your answer is correct!