This question comes from ch.7.3 titled :Adding and subtracting rational Expressions with the same denominator and least common denominator.

1/(10x

^{4}) + 4/5xLike 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.

10x

^{4}= 2*5*x^{4}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 x

^{4}:LCD = 2*5*x

^{4}= 10x^{4}To add then, we must change the denominator of the second expression to 10x

^{4}by multiplying it by the prime factors of the LCD it is missing, which is 2*x^{3}:1/(10x

^{4}) + (4/5x)(2x^{3}/2x^{3}) = 1/(10x^{4}) + (8x^{3})/(10x^{4}) = (1 + 8x^{3})/10x^{4}
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