SOLUTION: I am not understanding two questions on a teacher generated worksheet. The problems are to Solve the following equations: {{{a - 1 over a^2 - 4 plus 1 over a - 2 equals a + 4 ov

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am not understanding two questions on a teacher generated worksheet. The problems are to Solve the following equations: {{{a - 1 over a^2 - 4 plus 1 over a - 2 equals a + 4 ov      Log On


   



Question 131646: I am not understanding two questions on a teacher generated worksheet. The problems are to Solve the following equations:
a+-+1+over+a%5E2+-+4+plus+1+over+a+-+2+equals+a+%2B+4+over+a+%2B+2
x%5E2+%2B+7x+%2B+12+over+2x+%2B+6+times+x+over+x%5E2+-+16
I am so struggling with this concept. Any help would be greatly appreciated

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following equations:
(a - 1) /( a^2 - 4) + 1 /(a - 2) = (a + 4) /(a + 2)
Multiply thru by (a^2-4) to get:
(a-1) + (a+2) = (a+4)(a-2)
2a+1 = a^2+2a-8
a^2=9
a=3 or a=-3
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(x^2+7x+12)/(2x+6)*(x/(x^2-16)
Factor where you can:
= [(x+3)(x+4)/2(x+3)]
Cancel the (x+3) and the (x+4) factors to get:
= [1/2] * [x/(x-4)]
= x/[2(x-4)]
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Cheers,
Stan H.