1/x-1 + 1/x+2 = 5/4

solve for all solutions?

Question

1/x-1 + 1/x+2 = 5/4

solve for all solutions?

anonymous · Answer

Multiply both sides by 4(x-1)(x+2) and see what you can get

anonymous · Answer

$$
4 (x-1) (x+2)
   \left(\frac{1}{x+2}+\frac{1}{
   x-1}\right)=\frac{5}{4} 4
   (x-1) (x+2)
$$

anonymous · Answer

$$
\frac{4 (x-1)
   (x+2)}{x-1}+\frac{4 (x-1)
   (x+2)}{x+2}=\frac{5}{4} 4
   (x-1) (x+2)
$$
Simplify now.

anonymous · Answer

$$
4 (x-1)+4 (x+2)=5 (x-1) (x+2)
$$

anonymous · Answer

$$
8 x+4=5 x^2+5 x-10
$$

anonymous · Answer

Can you finish it now?

anonymous · Answer

yeah thx i understand now

hero · Answer

Actually x = 2 is one of the solutions since 2 + 2 = 4

anonymous · Answer

I thought x-2 was one of the denominator. I should have looked up.

hero · Answer

Yeah, I do the fractions on paper first before posting now to avoid mistakes like that. Actually, I have a technique that I use to make sure any extraneous roots are canceled before solving so I never run into that problem.

hero · Answer

And in this case, there were no extraneous roots.

anonymous · Answer

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