SOLUTION: Ok I have two questions that I have tried to work out but I keep going in circles..please help! 12. (3/x^2-5x+6)-(5/(x-2)^2) 28.{(1/x+h)-(1/x)/h}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Ok I have two questions that I have tried to work out but I keep going in circles..please help! 12. (3/x^2-5x+6)-(5/(x-2)^2) 28.{(1/x+h)-(1/x)/h}      Log On


   



Question 67827This question is from textbook College Mathematics for Business..
: Ok I have two questions that I have tried to work out but I keep going in circles..please help!
12. (3/x^2-5x+6)-(5/(x-2)^2)
28.{(1/x+h)-(1/x)/h}
This question is from textbook College Mathematics for Business..

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
12. (3/x^2-5x+6)-(5/(x-2)^2)
The least common denominator is (x-2)^2(x-3)
Rewrite each fraction with the lcd as its denominator as follows:
= 3(x-2)/lcd - 5(x-3)/lcd
Combine the numerators to get:
=[3x-6-5x+15]/lcd
=(-2x+9)/[(x-2)^2(x-3)]
===================================
28.{(1/x+h)-(1/x)/h}
lcd is h(x+h)
Rewrite the fractions to get:
= h/lcd - (1/x)(x+h))/lcd
Combine the numerators to get:
=[h -(1 + h/x)]/lcd
=[ (xh -x- h)/x]/lcd
=(xh-x-h)/[hx(x+h)]
Cheers,
Stan H.