Questions: Add and/or subtract and then simplify completely: 7x/(x^2-25) + x/(x+5)

Add and/or subtract and then simplify completely: 7x/(x^2-25) + x/(x+5)
Transcript text: Add and/or subtract and then simplify completely: \[ \frac{7 x}{x^{2}-25}+\frac{x}{x+5} \]
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Solution

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Solution Steps

To add and simplify the given expression, we first need to find a common denominator for the two fractions. Then, we can combine the fractions and simplify the resulting expression.

Step 1: Find a Common Denominator

Given:

  • \( fraction1 = \frac{7x}{x^2 - 25} \)
  • \( fraction2 = \frac{x}{x + 5} \)

The common denominator is \( (x + 5)(x^2 - 25) \).

Step 2: Combine Fractions

Combining the fractions, we get: \[ combined\_fraction = \frac{7x(x + 5)}{x^2 - 25} + \frac{x(x^2 - 25)}{x + 5} \]

Step 3: Simplify the Expression

Simplifying the expression, we have: \[ simplified\_expression = \frac{x(x^2 - 10x + 32)}{x^4 - 50x^2 + 625} \]

Final Answer

\[ \boxed{\frac{x(x^2 - 10x + 32)}{x^4 - 50x^2 + 625}} \]

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