Simplifying rational exp's: [(x + 3)/2]^2 - [(x - 3)/2]^2

[Chris*]

I'm having a little trouble with solving these expressions... Any help would be appreciated.

1. [ (x+3)/2 ]² - [(x-3)/2]²

2. 7/(x-3) [ 10/(x-1) - 5/(x-2) ] - [ 4/(x-2) ]

3. [m - (1/m)] / [ 1 - (1/m)]

 

[arthur ohlsten]

[[x+3]/2]^2 -[x-3]/2]^2
[x+3]^2/4 - [x-3]^2/4 place over common denominator 4
[ [x+3]^2-[x-3]^2]/4 square terms
[ [x^2+6x+9]-[x^2-6x+9] ]/4 combine terms
[12x]/4
3x

quick check let x=3 original = 9-0
checks for 1 value of x so probably correct

2)
[7/[x-3]] [10/[x-1] - 5/[x-2] ] - 4/[x-2]

lowest common denominator=[x-3][x-1][x-2]
place over lowest common denominator LCD
7[10][x-2] - 7[5][x-1] -4[x-1][x-3] all over LCD
70x-140 -35x+35 -4[x^2-4x+3] all over LCD
35x-105-4x^2+16x-12 all over LCD
-4x^2+51x-117 all over LCD
-[4x^2-51x+117] /[[x-1][x-2][x-3] ] factor
-[4x-39][x-3] /[[x-1][x-2][x-3]
-[4x-39] / [ [x-1][x-2] ]

3)
[m - 1/m] / [1-[1/m]]
place numerator and denominator over common denominators
[ [m^2-1]/m] / [[m-1]/m]
[m^2-1] /[m-1] factor
[ [m-1][m+1] ] / [m-1]
[m+1] answer

check at one point m=2
original [2-1/2] /[1-1/2] = 3/2 / 1/2 =3
m+1=3 probably correct

Arthur