Worksheet Add and Subtract Rational Expressions with answers.pdf ... - Free Printable

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To help you solve the problem, I’ll need either:

1. A clear description of the rational expressions you're supposed to add or subtract.
2. The text version of the problems from the worksheet.
3. A clearer image or a direct copy of the math problems.

However, I can still provide a general explanation of how to add and subtract rational expressions so you can apply it to your worksheet.

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🔧 How to Add/Subtract Rational Expressions

Rational expressions are fractions where the numerator and denominator are polynomials. To add or subtract them, follow these steps:

#### ✔ Step 1: Factor all denominators
Break down each denominator into its simplest factors.

#### ✔ Step 2: Find the Least Common Denominator (LCD)
The LCD is the smallest expression that contains all the factors of each denominator.

#### ✔ Step 3: Rewrite each fraction with the LCD as the denominator
Multiply the numerator and denominator of each fraction by whatever is missing to get the LCD.

#### ✔ Step 4: Combine the numerators
Add or subtract the numerators, keeping the common denominator.

#### ✔ Step 5: Simplify the result
Factor the numerator and cancel any common factors with the denominator.

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📌 Example Problem:

Let’s say one of the problems is:

$$
\frac{2}{x+3} + \frac{5}{x-1}
$$

#### Step 1: Factor denominators
Already factored: $ x+3 $ and $ x-1 $

#### Step 2: LCD = $ (x+3)(x-1) $

#### Step 3: Rewrite each fraction:
$$
\frac{2}{x+3} \cdot \frac{x-1}{x-1} = \frac{2(x-1)}{(x+3)(x-1)}
$$
$$
\frac{5}{x-1} \cdot \frac{x+3}{x+3} = \frac{5(x+3)}{(x+3)(x-1)}
$$

#### Step 4: Add numerators:
$$
\frac{2(x-1) + 5(x+3)}{(x+3)(x-1)} = \frac{2x - 2 + 5x + 15}{(x+3)(x-1)} = \frac{7x + 13}{(x+3)(x-1)}
$$

#### Step 5: Simplify
No common factors → Final answer:
$$
\boxed{\frac{7x + 13}{(x+3)(x-1)}}
$$

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💡 Tips:

- Always check for restrictions (values of $ x $ that make the denominator zero).
- Never cancel terms across addition/subtraction — only factor and cancel in multiplication/division.

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👉 Please reply with the actual problems from the worksheet (or describe them), and I’ll walk you through solving each one step-by-step!