Expert: NUR ARINA BASILAH BINTI KAMISAN - 8/23/2008

Question
1     1     5   
--- + --- = ---
x-1   x+2    4          find all real solutions to the equation

Answer
dear ashlee,

you have the equation above,
1/(x-1)+1/(x+2)=5/4
now do some multiplication on the left side so that both will have same number at the below part.

[(x+2)/(x-1)(x+2)]+[(x-1)/(x-1)(x+2)]=5/4
or we also can wite it in this form:
[(x+2)+(x-1)]/(x-1)(x+2)]=5/4
2x+1/(x-1)(x+2)=5/4
2x+1/(x^2+x-2)=5/4
now bring the equation above to right side
2x+1=5/4(x^2+x-2)
2x+1=5/4x^2+5/4x-5/2
now bring the left side to the right side and you will have:
0=5/4x^2+5/4x-5/2-2x-1
0=5/4x^2-3/2x+1/4
0=[5x^2-6x+1]/4
0*4=5x^2-6x+1
0=(5x-1)(x-1)
so 5x-1=0 or x-1=0
x=1/5 or x=1

the solution is x=1/5 and 1

write it back in a paper and try to understand this ok.good luck!!!