CALEBPROF

Error in mathematics Today I will show you Common mistake made in Algebraic. and ways to go about them Error     Correct/Justification/Example $$ \frac{2}{0} \neq 0 \text{ and } \frac{2}{0} \neq 2 $$ Division by zero is undefined \begin{align}  -3^2 & \neq  9 \\ \text{But} \\ (-3)^2 & = 9 \\ \text{ and} \\ -3^2 & = -9 \end{align} Watch parenthesis! \begin{align} (x^2)^3 & \neq  x^5 \quad \text{but} \\ (x^2)^3 & = x^2x^2x^2 \\ & = x^6 \end{align} \begin{align} \frac{a}{b+c} \neq & \frac{a}{b} + \frac{a}{c} \\ _ \text{Clear Example below} \\ \rightarrow\ \frac{1}{2} & = \frac{1}{1+1} \\ \text{but} \quad \frac{1}{1+1} & \neq \frac{1}{1} + \frac{1}{1} \\ \frac{1}{1} + \frac{1}{1} & = 2 \end{align} $$ \frac{1}{x^2+x^3} \neq x^{-2} + x^{-3} $$ A more complex of the previous error $$ -a(x-1) \neq -ax-a \quad \t...

Topic Overview When solving an equation, you are trying to find a  solution  which will make a particular mathematical equation  true  or  correct . For example: x - 3 = 2 If you put 5 in place of x; 5 - 3 = 2 This solution is true, therefore x = 5 is a solution of this equation. In the example above, there is only one solution for x. However, during your  maths working, you will be asked to solve various equations which have multiple solutions. For example: (x-4)(x-3)= 0 If x is 4, the solution to the equation is: (4-4)(4-3)=0 = 0 x 1= 0 When x is 3, the solution to the equation is: (3-4)(3-3)=0 = -1 x 0 = 0 Both of these solutions make the results of the equation true, therefore the solutions to this equation are  x = 4  or  3 Key Concepts In your working, you will be required to solve various mathematical equations. but as a rule you will be required to: Recognise the different symbols within al...