Question

Find the errors and correct the mathematical expression:
\[\dfrac{{4x + 5}}{{4x}} = 5\]

Answer 1

Hint: In a mathematical expression, when we are provided with a rational number and we have a polynomial term in the numerator with a common denominator, then the numerator can be written as splitted into two parts.
i.e. $ \dfrac{{Ax + B}}{C} = \dfrac{{Ax}}{C} + \dfrac{B}{C} $

Complete step-by-step answer:
1. We are provided with the expression:
\[\dfrac{{4x + 5}}{{4x}} = 5\]
2. L.H.S = \[\dfrac{{4x + 5}}{{4x}}\]
And, R.H.S = \[5\]
Since L.H.S $ \ne $ R.H.S
The mathematical expression is not correct
3. The correct expression would be:
\[\begin{gathered}
   = \dfrac{{4x + 5}}{{4x}} \\
   = \dfrac{{4x}}{{4x}} + \dfrac{5}{{4x}} \\
   = 1 + \dfrac{5}{{4x}} \\
\end{gathered} \]
Hence, L.H.S = R.H.S

Note: Just like we did in the question, as the numerator splits in two parts because the denominator was common, the visa-versa case is not possible.