Question

which shows the expressions rewritten with the least common denominator?\\(\frac{7x - 2}{4x^2}\\) and \\(\frac{x - 1}{8x}\\)\\(\frac{28x^2 - 8x}{16x^3}\\) and \\(\frac{2x^3 - 2x^2}{16x^3}\\)\\(\frac{14x - 4}{8x^2}\\) and \\(\frac{2x - 2}{8x^2}\\)\\(\frac{28x - 8}{16x^2}\\) and \\(\frac{2x^2 - 2x}{16x^2}\\)\\(\frac{14x - 4}{8x^2}\\) and \\(\frac{x^2 - x}{8x^2}\\)

Explanation:

Step1: Factor denominators

First denominator: $4x^2 = 4 \cdot x^2$
Second denominator: $8x = 8 \cdot x = 2^3 \cdot x$

Step2: Find least common denominator (LCD)

LCD is the product of highest powers of all factors: $8x^2$

Step3: Rewrite first fraction

Multiply numerator/denominator of $\frac{7x-2}{4x^2}$ by 2:
$\frac{(7x-2) \cdot 2}{4x^2 \cdot 2} = \frac{14x-4}{8x^2}$

Step4: Rewrite second fraction

Multiply numerator/denominator of $\frac{x-1}{8x}$ by $x$:
$\frac{(x-1) \cdot x}{8x \cdot x} = \frac{x^2 - x}{8x^2}$

Answer:

$\frac{14x-4}{8x^2}$ and $\frac{x^2-x}{8x^2}$ (the bottom option)