help me solve rational equations?

Question

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





2. 3/y-2 + 2y/4-y^2 = 5/y+2


can u please help me with these 2 problems..? thank u everyone!

Answer 1

1.
x/(x-2) + x/(x^2-4) = (x+3)/(x+2)
x/(x-2) + x/[(x-2)(x+2)] = (x+3)/(x+2)

Multiply everything by (x + 2)(x - 2)

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

2.
3/(y-2) + 2y/(4-y^2) = 5/(y+2)
3/(y-2) + 2y/[(2-y)(2+y)] = 5/(y+2)
-3/(2-y) + 2y/[(2-y)(2+y)] = 5/(y+2)

Multiply everything by (y + 2)(2 - y)

(-3)(y + 2) + 2y = 5(2 - y)
-3y - 6 + 2y = 10 - 5y
-y - 6 = 10 - 5y
4y - 6 = 10
4y = 4
y = 1

Answer 2

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

find the common denominator..which is... x^2-4 or (x+2)(x-2)

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

since the bottom is all the same.. u can ignore it ...& then just solve for x
x(x+2)+x=(x+3)(x-2)
x= -5/3


2.

2. common denom= 4-y^2
-3/(2-y) + 2y/9(2-y)(2+y)) = 5/(y+2)

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

solve

4y = 4
y = 1

Answer 3

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

lcd is x-2 x+2

x(x-2)+x=(x+3)(x+2)
x^2-2x+x=x^2+5x+6
x^2-x^2-x=x^2-x^2+5x+6
-x=5x+6
-x-5x=5x-5x+6
-6x=6
-6x/-6=6/-6
x=-1

2. 3/y-2 +2y/4-y^2=5(y+2)
lcd is y-2 y+2

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

3y+6+2y=5y-10
5y+6=5y-10
0y=-16

no solution -16/0 undefined