Question

which shows the rational expression written using the least common denominator? \\(\frac{x + 1}{4x^2} + \frac{x + 1}{x^2}\\) \\(\frac{x + 1}{x^2} + \frac{4(x + 1)}{x^2}\\) \\(\frac{x + 1}{x^2} + \frac{x + 1}{x^2}\\) \\(\frac{x + 1}{4x^2} + \frac{(x + 1)}{4x^2}\\) \\(\frac{x + 1}{4x^2} + \frac{x + 1}{4x^2}\\)

Explanation:

Step1: Identify denominators

Denominators are $4x^2$ and $x^2$.

Step2: Find least common denominator

The least common multiple of $4x^2$ and $x^2$ is $4x^2$.

Step3: Rewrite second fraction

Multiply numerator/denominator of $\frac{x+1}{x^2}$ by 4: $\frac{4(x+1)}{4x^2}$

Step4: Rewrite the expression

Combine with the first fraction.

Answer:

$\frac{x+1}{4x^2} + \frac{4(x+1)}{4x^2}$