Question

Calculate the following quotients:

A) 50x^4 : 25x^5 / 28y^6 : 14y^12
B) x^2 : x^2 + xy / xy - y^2 : x^2 - y^2
C) 8x^2y : 24xya / 13a : 26a^3
D) a^2 + 2ab + b^2 : a + b / a^2 - b^2 : a - b

Answer 1

To divide fractions with variables, invert the second fraction and multiply. Subtract exponents when dividing variables with the same base. Factor the expressions to simplify fractions. Cancel out common factors in the numerator and denominator of an expression.

Step-by-step explanation:

A)
To divide the given expression, we can invert the second fraction and multiply. When dividing exponents with the same base, we subtract the exponents. Therefore, the quotient is 2x^4y^12.

B)
To divide the given expression, we invert the second fraction and multiply. Since the expression has variables in the denominator, we need to factor them. The quotient simplifies to -1.

C)
To divide the given expression, we invert the second fraction and multiply. The variable 'a' cancels out. The quotient simplifies to rac{8x^2y}{26a^2}.

D)
To divide the given expression, we invert the second fraction and multiply. The numerator and denominator have a common factor of 'a + b'. The quotient simplifies to rac{a + b}{a - b}.