Question

which shows the expressions rewritten with the least common denominator? \\(\frac{2p - 5}{4p}\\) and \\(\frac{5p}{6p^2}\\) \\(\frac{6p^2 - 15p}{12p^2}\\) and \\(\frac{10p}{12p^2}\\) \\(\frac{6p - 15}{12p^2}\\) and \\(\frac{15p}{12p^2}\\) \\(\frac{6p - 15}{12p}\\) and \\(\frac{10p}{12p}\\) \\(\frac{6p^3 - 15p^2}{12p^3}\\) and \\(\frac{10p^2}{12p^3}\\)

Explanation:

Step1: Find denominators' factors

Denominators: $4p = 2^2 \cdot p$, $6p^2 = 2 \cdot 3 \cdot p^2$

Step2: Calculate least common denominator (LCD)

LCD = $2^2 \cdot 3 \cdot p^2 = 12p^2$

Step3: Rewrite first expression

Multiply numerator/denominator by $3p$:
$\frac{(2p-5) \cdot 3p}{4p \cdot 3p} = \frac{6p^2 - 15p}{12p^2}$

Step4: Rewrite second expression

Multiply numerator/denominator by $2$:
$\frac{5p \cdot 2}{6p^2 \cdot 2} = \frac{10p}{12p^2}$

Answer:

$\frac{6p^2 - 15p}{12p^2}$ and $\frac{10p}{12p^2}$