If x\ne 0, then \dfrac{x+1}{6x}+\dfrac{x+1}{2x}=

✓
\dfrac{2x+2}{3x}

×
\dfrac{2x+2}{4x}

×
\dfrac{2x+3}{6x}

×
\dfrac{2x+2}{8x}

×
\dfrac{x+2}{6x}
If x\ne 0, then \dfrac{x+1}{6x}+\dfrac{x+1}{2x}=
\dfrac{2x+2}{3x}
\dfrac{2x+2}{4x}
\dfrac{2x+3}{6x}
\dfrac{2x+2}{8x}
\dfrac{x+2}{6x}
Find a common denominator for the two fractions. 1/6x and 1/2x has a common denominator 6x .
There's no need to do anything for the fraction \dfrac{x+1}{6x}. But for \dfrac{x+1}{2x} , multiply 3 with both of its denominator and numerator.
Once the denominators are the same, add the numerators of both fractions. So,
\dfrac{x+1}{6x}+\dfrac{x+1}{2x}
= \dfrac{x+1}{6x}+\dfrac{3x+3}{6x}
=\dfrac{2x+2}{3x}