add. express your answer in simplest form x^2 over x+4 plus 2x-8 over x+4?

Question

also add 3y over y^2+5y +4 plus 2y over y^2-1

Answer 1

since they have the same denominator, you can just add the numerators:

(x^2 +2x -8)/ (x+4)

the numerator factors:
(x+4)(x-2)

the (x+4)'s cancel, leaving:

x-2


3y over y^2+5y +4 plus 2y over y^2-1

these need common denominators:
(y^2 +5y + 4) = (y+4)(y+1)
(y^2 -1) = (y-1)(y+1)

you need to multiply by (y+4)(y+1)(y-1)

(3y)(y-1) + (2y)(y+4)
----------- ---------------- =
(y+4)(y+1)(y-1)

3y^2 -3y + 2y^2 + 8y
------------- -------------- =
(y+4)(y+1)(y-1)

5y^2 + 5y
-------------- =
(y+4)(y+1)(y-1)

5y(y+1)
---------- =
(y+4)(y+1)(y-1)

the y+1 cancels, leaving:

(5y)/ [(y+4)(y-1)]

or you could multiply it out:
5y / (y^2 +3y -4)

Answer 2

x^2/(x+4) + (2x-8) / (x+4)
(x^2 + 2x-8) / (x+4)
(x + 4)(x-2) / (x+4)
x - 2

3y / (y^2+5y +4) + 2y / (y^2-1)
3y / (y+4)(y+1) + 2y / (y+1)(y-1)
3y(y-1) / (y+4)(y+1)(y-1) + 2y (y+4) / (y+1)(y-1)(y+4)
(3y(y-1) + 2y (y+4)) / (y+1)(y-1)(y+4)
(3y^2-3y + 2y^2+8y) / (y+1)(y-1)(y+4)
(5y^2-5y) / (y+1)(y-1)(y+4)
5y(y-1) / (y+1)(y-1)(y+4)
5y / (y+1)(y+4)

Answer 3

x^2/ x+4 + 2x-8/ x+4

x+4 is your lcd

x^2+2x-8
-------------
x+4

(x+4)(x-2)
-------------
x+4

the 2 x+4 cancel out leaving you x-2 as your answer

3y/y^2+5y+4 + 2y/ y^2-1

3y/ (y+1)(y+4) +2y / (y+1)(y-1)

lcd is y+1 y+4 y-1

3y(y-1) +2y (y+4)
3y^2-3y+2y^2+8y
5y^2+5y

5y^2+5y
-----------------
(y-1)(y+1)(y+4)

5y(y+1)
========
(y-1)(y+1)(y+4)

y+1 cancel out

5y / (y-1)(y+4)
5y / y^2+3y-4 answer

Answer 4

[(x² - 9)/(2x - 8)] / [(3 - x)/(x - 4)] = [(x² - 9)/(2x - 8)] * [(x - 4)/(3 - x)] = [(x² - 9) ( x - 4)] / [(3 - x)(2x - 8)] = [(x - 3)(x + 3)( x - 4)] / [(- a million)(x - 3)2(x - 4)] = [(x - 3)(x + 3)( x - 4)] / [(- 2)(x - 3)(x - 4)] if x ? 3 and x ? 4 = (x + 3) / (- 2) Alejandra