Question

Find and correct the errors in the mathematical statement $\frac{(3x^2+1)}{3x^2}=1+1=2$

Answer 1

Find and correct errors in the given statement

An equation is a mathematical expression of equality between two algebraic expressions that have equal values.

Given, $\frac{(3x^2+1)}{3x^2}=1+1=2$

On solving L.H.S, we get,

$$\begin{gathered} =\frac{3x^2+1}{3x^2} \\ =\frac{3x^2}{3x^2}+\frac{1}{3x^2} \\ =1+\frac{1}{3x^2} \end{gathered}$$

But, it is given that R.H.S $=1+1=2$

Thus, L.H .S.$\ne$ R.H.S.

So,for correct statement we need to replace $1+1$ with $1+\frac{1}{3x^2}$in RHS.

Hence, the correct statement is $\frac{\mathbf{(}\mathbf{3}{\mathbf{x}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}\mathbf{1}\mathbf{)}}{\mathbf{3}{\mathbf{x}}^{\mathbf{2}}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\mathbf{}\mathbf{+}\mathbf{}\frac{\mathbf{1}}{\mathbf{3}{\mathbf{x}}^{\mathbf{2}}}\mathbf{}$.