This question comes from ch.7.3 titled :Adding and subtracting rational Expressions with the same denominator and least common denominator.
1/(10x4) + 4/5x
Like any fraction, you can only add or subtract two rational expressions if they have the same denominator. To find the LCD, you have to do a "prime factorization", factoring each denominator down to its prime numbers.
10x4 = 2*5*x4
5x = 5*x
The LCD includes each unique prime factor. If a factor appears in more than one denominator, then choose the factor with the highest power. So for the above case, the unique prime factors are 2, 5, and x4:
LCD = 2*5*x4 = 10x4
To add then, we must change the denominator of the second expression to 10x4 by multiplying it by the prime factors of the LCD it is missing, which is 2*x3:
1/(10x4) + (4/5x)(2x3/2x3) = 1/(10x4) + (8x3)/(10x4) = (1 + 8x3)/10x4