Question

Find and correct errors of the following mathematical expression:
 $ \dfrac{{7x + 5}}{5} = 5 $

Answer 1

Hint: When we are provided with a rational number with a numerator of the form of a polynomial term and it shares the common denominator, then the numerator can be 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{{7x + 5}}{5} = 5 $
2. Here, L.H.S = $ \dfrac{{7x + 5}}{5} $
And, R.H.S = $ 5 $
Since, L.H.S $ \ne $ R.H.S
3. The correct mathematical expression would be:
 $ \begin{gathered}
   = \dfrac{{7x + 5}}{5} \\
   = \dfrac{{7x}}{5} + \dfrac{5}{5} \\
   = \dfrac{{7x}}{5} + 1 \\
\end{gathered} $
Therefore, L.H.S = R.H.S

Note: The mathematical expression in the question has a polynomial expression and with a common denominator can be splitted into two with respect to while keeping the denominator common. But, the visa-versa will not be true.