Question

Find and correct errors of the following mathematical expressions:
 $ \dfrac{{3x}}{{3x + 2}} = \dfrac{1}{2} $

Answer 1

Hint: In an expression if we have a rational number, and the denominator shares a common numerator, the denominator never splits up.
i.e. $ \dfrac{A}{{Bx + C}} \ne \dfrac{A}{{Bx}} + \dfrac{A}{C} $

Complete step-by-step answer:
1. We are provided with the expression:
 $ \dfrac{{3x}}{{3x + 2}} = \dfrac{1}{2} $
2. Since, L.H.S = $ \dfrac{{3x}}{{3x + 2}} $
And, R.H.S = $ \dfrac{1}{2} $
Therefore, L.H.S $ \ne $ R.H.S
And since the denominator also cannot be splitted into two parts according to the hint provided to us,
3. The correct expression would be:
 $ \dfrac{{3x}}{{3x + 2}} = \dfrac{{3x}}{{3x + 2}} $

Note: The denominator never splits into two parts.
It’s the numerator only which splits into two depending on the arithmetic operator used between.