Question

Find the LCD of the pair of expressions 1/2; 4/x^2

A 4x^2
B. 2x^2
C. 2x
D. C^2

Find the LCD of the pair of expressions 8/5b;12/7b^3c

Find the LCD of the pair of expressions 3m/m+n;3n/m-n

Add 7/3a+2/5

Add a/a+3+a+5/4

Add. 9+x-3/x+2

Answer 1

To find the Least Common Denominator (LCD) of rational expressions, we choose the higher power of exponent for similar factors and for the factors they don't share, we just multiply it to find the LCD. It's best to show this by answering the problems provided.

For the first one, we have


`(1)/(2) | (4)/(x^(2))`

since both denominators 4 and x² do not share any common factor, we just multiply them to find the LCD. So, we have A. 4x².

For the next item, we have


`(8)/(5b) | (12)/(7b^(3)c)`

we first check the coefficients of the denominators 5 and 7. Since they don't share any common factor, the LCD must have a coefficient of 7(5) = 35. As for the expressions, b and b³c, since they share a common factor of b, we choose the one with the greater exponent. Finally, we have an LCD of 35(b)(c) = 35b³c.

Following the same rules, the LCD of 3m/ (m + n) and 3n/ (m - n) is (m + n)(m -n ).

Adding rational expressions is similar to adding fractions. First, we get the LCD of the expression then express it so that both expressions have a common denominator.

So, we have


`(7)/(3a) + (2)/(5)`

`(7(5))/(15a) + (2(3a))/(15a)`

`\mathbf{(35 + 6a)/(15a)}`

For the next item,


`(a)/(a+3) + (a+5)/(4)`

`(4(a))/(4(a+3)) + ((a+5)(a+3))/(4(a+3))`

`(4a + (a+5)(a+3))/(4(a+3))`

`(4a + a^(2) +8a + 15)/(4(a+3))`

`\mathbf{(a^(2) + 12a + 15)/(4(a+3))}`

Lastly, we have


`9 + (x-3)/(x+2)`

`(9(x+2))/(x+2) + (x-3)/(x+2)`

`(9x + 18 + x - 3)/(x+2)`

`\mathbf{(10x + 15)/(x+2)}`