# sum of solutions?

• Oct 28th 2008, 12:17 PM
sum of solutions?
Solve:

5/(x+4) = 4 + [3/(x-2)]

What is the sum of your solutions?
• Oct 28th 2008, 12:33 PM
abey_27

the sum of your solutions is 6x + 10x - 4x squared..

if you were to solve this you get x equal to 2.5 or -1

hope that helps
• Oct 28th 2008, 12:48 PM
krystaline86
Quote:

Solve:

5/(x+4) = 4 + [3/(x-2)]

What is the sum of your solutions?

Make a common denominator by multiplying all the denominators to make one. So (x+4)(1)(x-2) will give you a denominator of (x+4)(x-2)

now you'll have
(something)/(x+4)(x-2) = (something)/(x+4)(x-2) + (something)/(x+4)(x-2)

to find out what that something is, make each term so that it denominator is this common one we just found.
1) term 5/(x+4) ---> [5(x-2)]/[(x+4)(x-2)]
2) term 4 ---> [4(x+4)(x-2)]/[(x+4)(x-2)]
3) term 3/(x-2) ---> [3(x+4)]/(x+4)(x-2)]
so now you have your terms, where their numerators can be added or subtracted with eachother since they all have like denominators.

[5(x-2)]/[(x+4)(x-2)] = [4(x+4)(x-2) + 3(x+4)]/[(x+4)(x-2)]
expand the numerator on each side. don't worry about the denominator since it's the same everywhere.

so, 5x-10 = 4(x^2+4x-2x-8) + 3x+12
5x-10 = 4x^2+16x-8x-32+3x+12
5x-10 = 4x^2+11x-10

So the question is... how do we make these two sides equal. Well, there's a number x which makes this possible. What's this number x? Let's find out. Bring all terms to one side, to start:
0 = 4x^2+11x-10-5x+10
0 = 4x^2+6x
0 = 2x(2x+3)
0 = 2x and 0 = 2x+3
So x = 0 and x = -3/2

There are two numbers that when substitued in for x, will make your original equation true.

Did that help, because I'm not too sure what you were specifically asking.
• Oct 28th 2008, 01:10 PM
Yes! thanks a lot
• Oct 28th 2008, 01:38 PM
abey_27
• Oct 28th 2008, 01:45 PM
krystaline86
No problem! (Clapping)
• Oct 28th 2008, 02:37 PM
pythag
Sum of solutions.
Quote:

Solve:

5/(x+4) = 4 + [3/(x-2)]

What is the sum of your solutions?

The sum of the solutions is -1.5 or -3/2.

LCM = (x+4)(x-2) , x not equal to -4; 2

5(x-2) = 4(x+4)(x-2) + 3(x+4)
5x-10 = 4(x^2 +2x-8)+3x+12
0 = 4x^2 +8x-32+3x+12-5x+10
0 = 4x^2 +6x-10
0 = 2x^2 +3x-5
0 = (2x+5)(x-1)

x=-5/2 or x=1 (these are the solutions)

the sum of the solutions
= -5/2 + 1
= -2.5 + 1
= -1.5

(I hope there aren't any mistakes...nice question. Cheers(Cool))