SOLUTION: 1. Add 1/1-x^2 + 1/x-1 2. Subtract 4x+1/25x^2+15x+2

Click here to see ALL problems on Exponents

Question 86129: 1. Add
1/1-x^2 + 1/x-1
2. Subtract
4x+1/25x^2+15x+2 - 3x-2/30x^2+11x+1
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
1. Add
1/(1-x^2) + 1/(x-1)
lcm = 1-x^2 = (1-x)(1+x)
= 1/lcm - (1+x)/lcm
=[1-1-x]/lcm
=-x/lcm
=x/(x^2-1)
===============
2. Subtract
(4x+1)/(25x^2+15x+2) - (3x-2)/(30x^2+11x+1)
= (4x+1)/[25x^2+5x+10x+2] - (3x-2)/[30x^2+5x+6x+1]
= (4x+1)/[5x(5x+1)+2(5x+1)] - (3x-2)/[5x(6x+1)+(6x+1)]
= (4x+1)/[(5x+1)(5x+2)] - (3x-2)/[(6x+1)(5x+1)]
lcm = (5x+1)(5x+2)(6x+1)
= [(4x+1)(6x+1)]/lcm - [(3x-2)(5x+2)]/lcm
= [ 24x^2+10x+1 - 15x^2+4x+4]/lcm
= [ 9x^2+14x+5]/lcm
= [9x^2+9x+5x+5]/lcm
= [9x(x+1)+5(x+1)]/lcm
= [ (x+1)(9x+5)]/[(5x+1)(5x+2)(6x+1)]
=======================
Cheers,
Stan H.

SOLUTION: 1. Add 1/1-x^2 + 1/x-1 2. Subtract 4x+1/25x^2+15x+2 - 3x-2/30x^2+11x+1