Question

Solve the equation.

Answer 1

\[(1/(x-1)) + (1/(x+2)) = 1/2\]

Answer 2

hmm what would be the LCD from \(\bf \cfrac{1}{x-1}+\cfrac{1}{x+2}?\)

Answer 3

[(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!

Answer 4

Does this all make sense to you?

Answer 5

Yes! Thank you so much.