Question

guided practice
write the factors of each denominator.
2p + 10 \t 2(p + 5)
p² - 25 \t (p + 5)(p - 5)
combining rational expressions
step 3
type your answer and then click or tap done.
use the symbol (shift+6 on the keyboard) to signify an exponent. for example, for 2 to the third power, enter 2^3.
simplify.
\frac{3p}{3(p + 5)} \cdot \frac{p - 5}{p - 5} + \frac{2}{(p + 5)(p - 5)} \cdot \frac{2}{2}

Explanation:

Step1: Identify common denominator

Common denominator is $2(p+5)(p-5)$

Step2: Rewrite terms with common denominator

$\frac{3p}{2(p+5)} \cdot \frac{p-5}{p-5} + \frac{2}{(p+5)(p-5)} \cdot \frac{2}{2} = \frac{3p(p-5) + 4}{2(p+5)(p-5)}$

Step3: Expand numerator

$3p(p-5) + 4 = 3p^2 -15p +4$? Correction: Wait original expression $\frac{3p}{2(p+5)} + \frac{2}{(p+5)(p-5)}$: correct expansion $\frac{3p(p-5) + 4}{2(p+5)(p-5)} = \frac{3p² -15p +4}{2(p+5)(p-5)}$? Wait no, original problem in image: $\frac{3p}{2(p+5)} + \frac{2}{(p+5)(p-5)}$ → common denominator $2(p+5)(p-5)$ → first term: $\frac{3p(p-5)}{2(p+5)(p-5)}$, second term: $\frac{4}{2(p+5)(p-5)}$ → numerator $3p² -15p +4$, denominator $2(p+5)(p-5)$. But if the problem was $\frac{3p}{2(p+5)} + \frac{2}{(p+5)(p-5)}$ simplified is $\frac{3p² -15p +4}{2(p+5)(p-5)}$. Wait maybe typo, but assuming standard:
Wait original image shows Step3: Simplify $\frac{3p}{2(p+5)} + \frac{2}{(p+5)(p-5)}$ → final simplified form is $\frac{3p² -15p +4}{2(p+5)(p-5)}$ (if no further factoring possible).

Wait correction: The correct steps for $\frac{3p}{2(p+5)} + \frac{2}{(p+5)(p-5)}$:

Step1: Find LCD

LCD = $2(p+5)(p-5)$

Step2: Adjust fractions to LCD

$\frac{3p(p-5)}{2(p+5)(p-5)} + \frac{2×2}{2(p+5)(p-5)}$

Step3: Combine numerators

$\frac{3p² -15p +4}{2(p+5)(p-5)}$

So final answer is $\frac{3p² -15p +4}{2(p+5)(p-5)}$ (if numerator doesn't factor).

Wait but maybe the original problem was different, but based on standard simplification of rational expressions, this is the result.

Wait the image's Step3 says "Simplify $\frac{3p}{2(p+5)} + \frac{2}{(p+5)(p-5)}$" → yes, so the answer is $\frac{3p² -15p +4}{2(p+5)(p-5)}$.

Step1: Determine LCD

LCD = $2(p+5)(p-5)$

Step2: Rewrite fractions with LCD

$\frac{3p(p-5)}{2(p+5)(p-5)} + \frac{4}{2(p+5)(p-5)}$

Step3: Combine numerators

$\frac{3p^2 -15p +4}{2(p+5)(p-5)}$

Answer:

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