Problem 48 - Introductory Algebra for College Students

Question

Add or subtract as indicated. Simplify the result, if possible. $$\frac{y}{y-5}-\frac{y-5}{y}$$

Step-by-Step Solution

Answer

\(\frac{5}{y-5}\) for y ≠ 0,5

Step 1: Finding Common Denominator

To be able to add or subtract fractions, they need to have the same denominator. In this case, the common denominator is \(y*(y-5)\)

Step 2: Rewriting with Common Denominator

Multiply each term in the fraction by necessary terms to achieve the common denominator: \[\frac{y*y}{y*(y-5)} - \frac{(y-5)*(y)}{y*(y-5)} = \frac{y^2}{y*(y-5)} - \frac{(y^2-5*y)}{y*(y-5)}\]

Step 3: Combining the Numerators

Since the denominators are the same, you can subtract the numerators: \[\frac{y^2-(y^2-5*y)}{y*(y-5)} = \frac{5*y}{y*(y-5)}\]

Step 4: Simplifying the Fraction

The expression is simplified by canceling out common terms in the numerator and the denominator, therefore, the answer is \[\frac{5}{y-5}\] when y ≠ 0,5