Question

Simplify completely quantity x squared minus 4 x plus 4 over quantity x squared plus 10 x plus 25 times quantity x plus 5 over quantity x squared plus 3 x minus 10.

Answer 1

Haha, this is more a problem of reading the question right :)

(x^2-4x+4)/(x^2+10x+25) * (x+5)/(x^2+3x-10)

Upon factoring the numerator and denominators...

[(x-2)^2/(x+5)^2]*(x+5)/((x+5)(x-2))  so on the right side the (x+5)s cancel

((x-2)^2/(x+5)^2)*1/(x-2)  which is:

[(x-2)^2]/[(x+5)^2*(x-2)]  now you can see that (x-2)^1 cancels

(x-2)/(x+5)^2  or if you prefer it expanded...

(x-2)/(x^2+10x+25)