Question

hw 12.2_add & subtract rational expressions
score: 10/17 answered: 10/17
question 11
simplify and reduce to the lowest terms. (leave answer in factored form.)
\\(\frac{5x}{x - 2} + \frac{3}{(x - 2)^2} =\\)

Explanation:

Step1: Find common denominator

The common denominator is $(x-2)^2$. Multiply numerator and denominator of $\frac{5x}{x-2}$ by $(x-2)$:
$\frac{5x}{x-2} = \frac{5x(x-2)}{(x-2)^2}$

Step2: Add the numerators

Combine the fractions over the common denominator:
$\frac{5x(x-2) + 3}{(x-2)^2}$

Step3: Expand and simplify numerator

Expand $5x(x-2)$ and combine like terms:
$5x(x-2) + 3 = 5x^2 - 10x + 3$

Answer:

$\frac{5x^2 - 10x + 3}{(x-2)^2}$