Question

Simplify ((4x²+12x-16)/(2x+10))/((6x+24)/(x²+9x+20))

Answer 1

The question involves simplifying a complex algebraic fraction by separately simplifying the numerator and denominator, factoring, and then multiplying by the reciprocal of the divisor to simplify further.

Step-by-step explanation:

The student's question is asking to simplify the given complex fraction:

((4x²+12x-16)/(2x+10))/((6x+24)/(x²+9x+20))

To solve this, we need to follow these steps:

1. Simplify the numerator and the denominator separately.
2. Factor where possible.
3. Multiply by the reciprocal of the divisor.
4. Multiply the numerators together and the denominators together.
5. Simplify by canceling out common factors.

This is a problem that requires knowledge of algebraic manipulation, including factoring, multiplying polynomials, and simplifying complex fractions.