Out of 20 problems, Two of them I can't get. Can you help?

Question

I have to find the Least Common Denominator and not combine the fractions: 12 / 5a^2 and 9 / a^3 The second set of fractions is: 13 / x^2 - 16 and 7 / x-4 Can you help?

Answer 1

1st set:

= 12/5a² and 9/a³

= (12[a])/(5a²[a]) and (9[5])/(a³[5])

= 12a/5a³ and 45/5a³

Answer: 5a³ is the least common denominator (LCD).

2nd set:

= 13/(x² - 16) and 7/(x - 4)

= 13/([x + 4][x - 4]) and 7/(x - 4)

= 13/([x + 4][x - 4]) and (7[x + 4])/([x + 4][x - 4])

= 13/(x² - 16) and (7x + 28)/(x² - 16)

Answer: x² - 16 or (x + 4)(x - 4) is the least common denominator (LCD):

Answer 2

I wish i knew...You must be really smart

Answer 3

PROBLEM 1:

5a^2 = 5 * a * a

a^3 = ...... a * a * a

LCD = 5 * a * a * a = 5a^3

12a / 5a^3 + 45 / 5a^3

Answer:

(12a + 45 ) / 5a^3

PROBLEM 2:

x² - 16 (difference of squares)

= (x - 4)(x + 4)

LCD = (x - 4)(x + 4) = x² - 16

13 / (x² - 16) + 7(x + 4) / (x² - 16)

= 13 / (x² - 16) + (7x + 28) / (x² - 16)

Answer:

(7x + 41) / (x² - 16)

Answer 4

1. 12/5a^2 and 9/a^3

        (12a+45)/5a^3

2. 13/x^2-16  and 7/x-4

Factor x^2-16

        

          x^2-16 = (x+4) (x-4)

this becomes your LCD

          [13 + 7(x+4)] / (x+4)(x-4)