Posted by **Unknown** on Tuesday, August 21, 2012 at 2:51pm.

Help Solving These?

There Are more like these ,

but i need examples to help me with the others.

1.5/2y+6 + 1/y-2=3/y+3

2. 3/3x-2 = 4/2x+1

3.5/3x - 1/9 = 1/x

4.2/x^2-x-12 -6/x+4 = 2/x-3

- Math -
**Morgan**, Tuesday, August 21, 2012 at 3:31pm
You will need to use the distributive property of multiplication.

5/(2y+6) + 1/(y-2) = 3/(y+3)

5/2(y+3) + 1/(y-2) = 3/(y+3)

2(5)/(y+3) + 2/(y-2) = 2(3)/(y+3)

10/(y+3) + 2/(y-2) = 6/(y+3)

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

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

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

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

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

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

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

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

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

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

-(7/2) = (3/2)y

-(7/2) / (3/2) = y

- (7/3) = y

y = - 2 1/3

- Math -
**Steve**, Tuesday, August 21, 2012 at 3:51pm
hmmm. I don't get that.

5/(2y+6) + 1/(y-2) = 3/(y+3)

putting all over 2(y+3)(y-2), and discarding the denominator, we have

5(y-2) + 2(y+3) = 3*2(y-2)

5y - 10 + 2y + 6 = 6y - 12

y = -8

check:

5/-10 + 1/-10 = 6/-10 = 3/-5

----------------------------

3/(3x-2) = 4/(2x+1)

putting all over (3x-2)(2x+1), we have

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

6x + 3 = 12x - 8

6x = 11

x = 11/6

-------------------------------

5/3x - 1/9 = 1/x

put all over 9x:

5*3 - x = 9

x = 6

------------------------------

2/(x^2-x-12) -6/(x+4) = 2/(x-3)

note that x^2-x-12 = (x-4)(x+3)

So, putting all over (x-4)(x+4)(x-3)(x+3), we have

2(x+4)(x-3) - 6(x+4)(x-3)(x+3) = 2(x-4)(x+4)(x+3)

Now, that's kind of nasty. I think you have a typo. If instead we have

2/(x^2+x-12) -6/(x+4) = 2/(x-3)

the LCD = (x+4)(x-3), and we get

2 - 6(x-3) = 2(x+4)

2 - 6x + 18 = 2x + 8

x = 3/2

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