Final answer:
To simplify the expression (2x-10)/(x+1) · (5+5x)/(15-3x), cancel the common factors after factoring to get the simplified result of -3⅗3/3.
Step-by-step explanation:
To perform the indicated operation and simplify the result for the expression (2x-10)/(x+1) · (5+5x)/(15-3x), we need to first factor where possible and then multiply the fractions. Let's do this step by step:
- Factor out common factors in the numerators and denominators. Here, we can factor out a 5 from the numerator of the second fraction: (5+5x) = 5(1+x).
- Recognize that (15-3x) can be factored to 3(5-x), and since (5-x) is -(x-5), we can write the second fraction's denominator as -3(x-5).
- Next, we observe that the expression (2x-10) in the numerator of the first fraction is 2(x-5), which will cancel out with the (x-5) in the second fraction's denominator.
- Now we have: [2(x-5)/(x+1)] · [5(1+x)/-3(x-5)]. Cancel out the (x-5) terms and the (1+x) terms which are common to a numerator and a denominator.
- The simplified form of our expression is then: (2/-3) · 5, which simplifies to -10/3 or -3⅗3/3.