anonymous
  • anonymous
Solve the equation.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[(1/(x-1)) + (1/(x+2)) = 1/2\]
jdoe0001
  • jdoe0001
hmm what would be the LCD from \(\bf \cfrac{1}{x-1}+\cfrac{1}{x+2}?\)
theopenstudyowl
  • theopenstudyowl
[(x+2+x-1)/(x-1)(x+2)]=1/2 2x+1/(x^2)+2x-x-2=1/2 2[(2x+1)/(x^2)+(2x-x-2)]=1/2(2) 4x+2/(x^2)+2x-x-2=1 divide both sides by the denominator of the ratio on the left side of the equation: becomes: 4x+2=(x^2)+2x-x-2 rotate equation: becomes: (x^2)+2x-x-2=4x+2 (x^2)+2x-4x-x=2+2 (x^2)-3x=4 x^2 - 3x-4=0 (x-4)(x+1)=0, therefore there are 2 solutions for x, x-4=0, x+1=0, x=4,-1, if you could not factor it on your own on a similar problem in the future... you could use the quadratic formula which I am sure you are familiar with... Hence: x=4 and x=-1 is your final solution! Happy Studying!

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theopenstudyowl
  • theopenstudyowl
Does this all make sense to you?
anonymous
  • anonymous
Yes! Thank you so much.

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