Final answer:
To simplify the expression (x²+8xy+15y²)/(5x-35y)*(x-7y)/(x²-xy-12y²), factor the numerator and denominator, and cancel out common factors to get (x+5y)/(x-4y).
Step-by-step explanation:
To simplify the expression (x²+8xy+15y²)/(5x-35y)*(x-7y)/(x²-xy-12y²), we can start by factoring each of the four polynomials involved. First, factor the numerator (x²+8xy+15y²) into (x+3y)(x+5y), and factor the denominator (x²-xy-12y²) into (x-4y)(x+3y). Then, simplify the expression by canceling out common factors. Cancel out (x+3y) from the numerator and denominator to get: (x+5y)/(x-4y).