Solve: 1/x + 3/x^2
Understand the Problem
The question asks us to add two algebraic fractions together. To solve this, we need to find a common denominator, adjust the numerators accordingly, and then combine the fractions.
Answer
$\frac{x+3}{x^2}$
Answer for screen readers
$\frac{x+3}{x^2}$
Steps to Solve
- Find the Least Common Denominator (LCD)
The denominators are $x$ and $x^2$. The LCD is $x^2$.
- Rewrite each fraction with the LCD
To rewrite $\frac{1}{x}$ with a denominator of $x^2$, we multiply both the numerator and denominator by $x$:
$$ \frac{1}{x} \cdot \frac{x}{x} = \frac{x}{x^2} $$
The second fraction, $\frac{3}{x^2}$, already has the LCD as its denominator, so we don't need to change it.
- Add the fractions
Now we can add the fractions:
$$ \frac{x}{x^2} + \frac{3}{x^2} = \frac{x+3}{x^2} $$
$\frac{x+3}{x^2}$
More Information
The expression $\frac{x+3}{x^2}$ is the simplest form of the given expression. We cannot simplify further as there are no common factors between the numerator and denominator.
Tips
A common mistake is to incorrectly identify the least common denominator or to forget to adjust the numerator when changing the denominator. In this case, students might forget to multiply the numerator of the first fraction by $x$ when changing the denominator to $x^2$.
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