Question

add. simplify, if possible.

\\(\frac{4}{y} + \frac{9}{y^2}\\)

\\(\frac{4}{y} + \frac{9}{y^2} = \square\\)

Explanation:

Identify the denominators

The given expression is:

$$ \frac{4}{y} + \frac{9}{y^2} $$

The denominators are \(y\) and \(y^2\).

Find the least common denominator

To add these rational expressions, we must find the least common denominator (LCD).
The LCD of \(y\) and \(y^2\) is \(y^2\).

Rewrite each fraction with the LCD

Multiply the numerator and denominator of the first fraction by \(y\) to obtain the common denominator:

$$ \frac{4 \cdot y}{y \cdot y} = \frac{4y}{y^2} $$

The second fraction already has the denominator \(y^2\):

$$ \frac{9}{y^2} $$

Add the numerators

Combine the numerators over the common denominator:

$$ \frac{4y}{y^2} + \frac{9}{y^2} = \frac{4y + 9}{y^2} $$

Simplify the expression

Check if the numerator \(4y + 9\) can be factored or simplified with the denominator \(y^2\).
Since \(4y + 9\) has no common factors with \(y^2\), the expression is in its simplest form.

Answer:

Add. Simplify, if possible.

\(\frac{4}{y} + \frac{9}{y^2} =\) <blank>\(\frac{4y+9}{y^2}\)</blank>