Question

There are a few problems on my homework im having trouble on. can you explain how to do these problems? thanks

1. x^2+10x+25-9y^2
2. x^2+2x-3
-------------
x^2+3x--2
3. 2xSQRT(x^2+5) - 2x^3/x^2+5
---------------------------------------
x^2+5

sorry #3 is kinda big. and gave me most trouble, #2 might actually be really easy but im probably overthinking it.

Answer 1

You do not say what to. Factor, reduce?
x^2+10x+25-9y^2
= (x+5)^2 - 9 y^2
so what?
if it were equal to something it might be a hyperbola :)

x^2+2x-3
-------------
x^2+3x+2

= [(x+3)(x-1)] / [(x+2)(x+1)]


2xSQRT(x^2+5) - 2x^3/(x^2+5)
---------------------------------------
(x^2+5)

2x [ SQRT(x^2+5) - x^2/(x^2+5)]
---------------------------------------
(x^2+5)

2x [ (x^2+5)^1.5 - x^2]
---------------------------------------
(x^2+5)

not much I see to do

Answer 2

1. x^2 + 10x + 25 - 9y^2.
x^2 + 10x + 25 is a perfect square:
(x+5)^2 - 9y^2. The difference of two squares.
((x+5) + 3y) * ((x+5)-3y).

2. x^2 + 2x - 3. Factor it:
(x+3)(x-1).