solve the ff complex algebraic expression
Answer (1)
Answer:The expression is: (a + b)/b - b/(a + b) divided by (1/b + 2/a) Step 1: Simplify the numerator - Find a common denominator for the two fractions in the numerator:- (a + b)/b - b/(a + b) = [(a + b)(a + b) - b²] / [b(a + b)]- Expand the numerator:- [(a + b)(a + b) - b²] / [b(a + b)] = (a² + 2ab + b² - b²) / [b(a + b)]- Simplify:- (a² + 2ab + b² - b²) / [b(a + b)] = (a² + 2ab) / [b(a + b)] Step 2: Simplify the denominator - Find a common denominator for the two fractions in the denominator:- (1/b + 2/a) = (a + 2b) / (ab) Step 3: Divide the simplified numerator by the simplified denominator - [(a² + 2ab) / [b(a + b)]] divided by [(a + 2b) / (ab)]- When dividing fractions, we invert the second fraction and multiply:- [(a² + 2ab) / [b(a + b)]] * [(ab) / (a + 2b)]- Simplify by canceling common factors:- (a² + 2ab) * (a) / [(a + b) * (a + 2b)] Step 4: Final Answer The simplified expression is a(a + 2b) / [(a + b)(a + 2b)]. This can be further simplified if you want to factor out any common terms.
