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...