Questions: Rational Expressions Adding rational expressions with common denominators Add. -((5x-5y)/(8x))+((2x-7y)/(8x)) Simplify your answer as much as possible.

Rational Expressions
Adding rational expressions with common denominators

Add.
-((5x-5y)/(8x))+((2x-7y)/(8x))

Simplify your answer as much as possible.

Transcript text: Rational Expressions Adding rational expressions with common denominators Add. \[ -\frac{5 x-5 y}{8 x}+\frac{2 x-7 y}{8 x} \] Simplify your answer as much as possible.

Solution

Solution Steps

To add rational expressions with common denominators, we simply add the numerators together while keeping the common denominator. After combining the numerators, we simplify the resulting expression if possible.

Solution Approach

Combine the numerators of the given rational expressions.
Simplify the resulting expression by combining like terms.
Keep the common denominator as it is.

Step 1: Combine the Numerators

We start with the two rational expressions: \[ -\frac{5x - 5y}{8x} + \frac{2x - 7y}{8x} \] Since they have a common denominator of \(8x\), we can combine the numerators: \[ -\left(5x - 5y\right) + \left(2x - 7y\right) = -5x + 5y + 2x - 7y \]

Step 2: Simplify the Combined Numerator

Now, we simplify the combined numerator: \[ -5x + 2x + 5y - 7y = -3x - 2y \]

Step 3: Form the Final Expression

The combined and simplified expression is: \[ \frac{-3x - 2y}{8x} \]