Subtracting Rational Expressions, HELP!?

Question

2/(5w+10) - 3/(2w-4)

Answer 1

2/(5w + 10) - 3/(2w - 4)

First thing you do is factor each denominator.

2/[5(w + 2)] - 3/[2(w - 2)]

This makes it obvious that the lowest common denominator is going to be (5)(2)(w + 2)(w - 2), so giving them a common denominator yields

{ [2(2)(w - 2)] - [3(5)(w + 2)] } / [(5)(2)(w + 2)(w - 2)]

Simplify the top,

{ 4(w - 2) - 15(w + 2) } / [10(w + 2)(w - 2)]

Simplify the top again,

{ 4w - 8 - 15w - 30 } / [10(w + 2)(w - 2)]

{-11w - 38 } / [10(w + 2)(w - 2)]

Answer 2

Just like adding or subtracting two fractions, you need to find a common denominator. The expressions (5w+10) and (2w+4) share no common factors, so the simplest common denominator is their product. So:

2/(5w+10) - 3/(2w-4)
= 2/(5w+10) * (2w-4)/(2w-4) - 3/(2w-4) * (5w+10)/(5w+10)
= 2(2w-4)/( (5w+10)(2w-4) ) - 3(5w+10)/( (5w+10)(2w-4) )
= ( 2(2w-4) - 3(5w+10) )/( (5w+10)(2w-4) )
= ( 4w-8-15w-30 )/(10w^2 - 20w + 20w - 40)
= (-11w - 38)/(10w^2 - 40).

Answer 3

2/(5w+10) -3/(2w-4)

first put the terms over a commmon denominator. The quickest way is to cross multiply though this may give you some large numbers to deal with:

(2(2w-4)- 3(5w+10))/((5w+10)(2w-4))

simplify:

(4w-8-15w-30)/(10w^2-40)
(-11w-38)/(10w^2-40)
(-11w-38)/(10{w^2-4})

Answer 4

You have to have a common denominator. In this case, factor both denominators. Factor a 5 out of the left one, and -2 out of the right one. This will give you 2/(5(w+2)) + 3/(2(w+2)). You now have a PLUS between the terms because of the negative 2 in the denominator on the right fraction. Next, multiply everything by 10 on the top to cancel the 5 and the 2. Now you have 4 plus 15 (or 19 when simplified) on top and 10(w+2) on the bottom, or 10w+20 if you multiply it out. Your final answer will be 19/(10w+20) or 19/(10(w+2), depending on what your teacher wants. Hope that was clear, it's hard to show work by typing!

Answer 5

numerator:
2(2w-4)-3(5w+10)
=4w-8-15w-30
=-11w-38

denominator:
(5w+10)(2w-4)
=10w^2-20w+20w-40
=10w^2-40

answer:
(-11w-38)/(10w^2-40)
you can take 10 out in the denominator.

Answer 6

X^2 + 2x _ x^2 +5x + 6 = x(x+2) _ x(x+2)(x+3) 3x 3x 3x 3x (x+2) _ (x+2)(x=+3) = (x+3) 3 3 3 the respond is (x+3) over 3 can't draw the lines between the numerator and the denominator yet you get the assumption.