Question

which shows the expressions rewritten with the least common denominator?\\(\frac{5x + 3}{3x}\\) and \\(\frac{7x}{2x^2}\\)\\(\frac{10x^2 + 6}{6x^2}\\) and \\(\frac{21x}{6x^2}\\)\\(\frac{20x^2 + 12x}{12x^2}\\) and \\(\frac{42x}{12x^2}\\)\\(\frac{20x + 12}{12x}\\) and \\(\frac{42}{12x}\\)\\(\frac{10x^2 + 6x}{6x^2}\\) and \\(\frac{21x}{6x^2}\\)

Explanation:

Step1: Find least common denominator

The denominators are $3x$ and $2x^2$. The least common multiple of 3 and 2 is 6, and the highest power of $x$ is $x^2$, so LCD = $6x^2$.

Step2: Rewrite first fraction

Multiply numerator/denominator of $\frac{5x+3}{3x}$ by $2x$:
$\frac{(5x+3) \cdot 2x}{3x \cdot 2x} = \frac{10x^2+6x}{6x^2}$

Step3: Rewrite second fraction

Multiply numerator/denominator of $\frac{7x}{2x^2}$ by 3:
$\frac{7x \cdot 3}{2x^2 \cdot 3} = \frac{21x}{6x^2}$

Answer:

$\frac{10x^2+6x}{6x^2}$ and $\frac{21x}{6x^2}$