Questions: Adding rational expressions with common denominators and Subtract. (-frac4 a+2 x6 a-frac9 a-8 x6 a)

Adding rational expressions with common denominators and Subtract. (-frac4 a+2 x6 a-frac9 a-8 x6 a)
Transcript text: Adding rational expressions with common denominators and Subtract. \[ -\frac{4 a+2 x}{6 a}-\frac{9 a-8 x}{6 a} \]
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Solution

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Solution Steps

Step 1: Write the Rational Expressions

We start with the two rational expressions that we need to subtract: \[ -\frac{4a + 2x}{6a} \quad \text{and} \quad -\frac{9a - 8x}{6a} \]

Step 2: Combine the Expressions

Since both expressions have a common denominator of \(6a\), we can combine them: \[ -\frac{4a + 2x}{6a} - \frac{9a - 8x}{6a} = \frac{- (4a + 2x) - (9a - 8x)}{6a} \]

Step 3: Simplify the Numerator

Now, we simplify the numerator: \[ -(4a + 2x) - (9a - 8x) = -4a - 2x - 9a + 8x = -13a + 6x \] Thus, we have: \[ \frac{-13a + 6x}{6a} \]

Step 4: Factor the Numerator

We can factor out a common factor from the numerator: \[ \frac{6x - 13a}{6a} = \frac{5(a - 2x)}{6a} \]

Final Answer

The simplified result of the subtraction is: \[ \boxed{\frac{5(a - 2x)}{6a}} \]

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