(x-5) / (x^2 -5x) - (x+5) / (x^2 - 25)?

Question

Subtract and simplify. Remember to include any changes in the domain

Answer 1

Step 1: Factor out the denominators and simplify each fraction.

Fraction 1:
(x - 5) / (x^2 - 5x)
Factor the denominator.
x^2 - 5x = x(x - 5)
(x - 5) / x(x - 5) = 1/x

Fraction 2:
(x + 5) / (x^2 - 25)
Factor the denominator.
(x^2 - 25) = (x + 5) (x - 5) (Subtraction of 2 squares)
(x + 5) / (x + 5) (x - 5) = 1/(x - 5)

Step 2: Find a common denomator for the 2 remaining fractions.
1 / x - 1/(x - 5)
1 / x * (x - 5)/(x - 5) - 1/(x - 5) * x/x
(x - 5) / (x(x - 5)) - x/(x - 5)

Step 3: Simplify.
(x - 5) / (x(x - 5)) - x/(x(x - 5))
- 5 / (x(x - 5))
- 5 / x^2 - 5x (solution!)

Answer 2

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