Question

(1 point)
find the lcd of the rational expressions:
(a) $\frac{2}{9b^{2}}$, $\frac{2}{9b^{5}}$:
(b) $\frac{5}{12b - 36}$, $\frac{6}{6b + 24}$:
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Explanation:

Step1: Analyze denominators in (a)

The denominators are $9b^{2}$ and $9b^{5}$. For the coefficient part, the LCM of 9 and 9 is 9. For the variable part $b^{2}$ and $b^{5}$, using the rule of LCM for powers of the same variable ($LCM(b^{m},b^{n})=b^{\max(m,n)}$), we take $b^{5}$. So the LCD is $9b^{5}$.

Step2: Factor denominators in (b)

Factor $12b - 36=12(b - 3)=2^{2}\times3\times(b - 3)$ and $6b + 24=6(b + 4)=2\times3\times(b + 4)$.

Step3: Find LCM of coefficients and factors

For the coefficients 12 and 6, the LCM of 12 and 6 is 12. For the binomial factors $(b - 3)$ and $(b + 4)$, since they are distinct, we include both. So the LCD is $12(b - 3)(b + 4)$.

Answer:

(a) $9b^{5}$
(b) $12(b - 3)(b + 4)$