1) Assuming x^2 – 4 and x+2 are intended as denominators, the problem should present as,

x / (x^2 – 4) + 1 / (x+2) = 3.

First, notice that x^2 – 4 factors to (x+2)(x-2). Thus the problem becomes,

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

If we multiply both sides by (x+2)(x-2), we have,

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

==> 2x – 2 = 3x^2 – 12

==> 3x^2 – 2x – 10 = 0

Solve for x, check for extraneous solutions, and you are done.

2) I am not going to guess how this equation should read. Without proper use of grouping symbols, communicating mathematics is ineffective.

3) Given |3x + 2| = 7, it follows that,

3x + 2 = 7 or 3x + 2 = -7. Solve each for x.

Regards,

Rich B.

if 3x+2 is positive we have:

3x+2=7

3x=5

x=5/3

if negative:

3x+2=-7

3x=-9

x=-3

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

x+1/3-x+1/x+2=0

1/3+1/x+2=0

1/x=-2-1/3

1/x=-7/3

x=-3/7

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

the x/x^2 is 1/x so we have

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

2/x-2=3

2/x=5

x=5/2

satisfied?