Multiply the following rational expressions.

Question

1. 3x²+15x/x²+x-12 • x⁵+5x²+4x/x²+4x-5x

2. x²-y²/x+1 • 5xy²+y²/2x²+2xy

Answer 1

1. Adding some parentheses:

(3x²+15x) (x⁵+5x²+4x) 3x(x+5) x(x⁴+5x+4). 3x(x+5) (x⁴+5x+4) (3x⁶+15x⁵+90x³+12x²+60x)

------------- * ---------------- = ------------- * ---------------- = ------------- * -------------- = ----------------------------------

(x²+x-12) (x²+4x-5x) (x+4)(x-3) x(x-1) (x+4)(x-3) (x-1) (x³-13x+12)

x cancels

2.Adding some parentheses:

(x²-y²) (5xy²+y²) (x+y)(x-y) y²(5x+1) y²(x-y)(5x+1) 5x² y²+5xy²-5x y³-y³

-------- • ------------ = ------------- • ------------ = ------------------= --------------------------

(x+1) (2x²+2xy) (x+1) 2x(x+y) 2x(x+1) 2x²+x

(x+y) cancels