from sympy import symbols, simplify

Define the variables

a, b = symbols('a b')

Define the algebraic expressions

expr1 = (15a - 35)/25 + 6a2/(3*a - 7) + a2/35 expr2 = 8/(b**2 - 4) + (b - 2)/(2b + 4) + 4/(2(b + 2)**2)

Simplify the expressions

simplified_expr1 = simplify(expr1) simplified_expr2 = simplify(expr2)

simplified_expr1, simplified_expr2Here are the simplified forms of the algebraic expressions:

1. The first expression simplifies to: $\frac{3a^3 + 266a^2 - 294a + 343}{35(3a - 7)}$

2. The second expression simplifies to: $\frac{\frac{1}{2}b^3 - b^2 + 8b + 16}{b^3 + 2b^2 - 4b - 8}$

Let me know if you need further details or have any questions.

Related Questions:

1. How would the expressions change if $a$ or $b$ had different constraints?
2. Can you factorize the numerators of the simplified expressions further?
3. How can these rational expressions be used in real-world applications?
4. What happens if $a = 0$ or $b = 0$ in these expressions?
5. How can we find the domain of the original and simplified expressions?

Tip: Always check for any restrictions in the denominator when simplifying rational expressions to avoid undefined expressions.