c) `(2x)/15=(-4)/5`
`⇒2x=((-4)*15)/5`
`⇒2x=-12`
`⇒x=-12:2`
`⇒x=-6`
Vậy `x=-6`
Bài 4:
`A=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(2016*2017)+1/(2017*2018)`
`A=1-1/2+1/2-1/3+1/3-1/4+...+1/2017-1/2018`
`A=1-1/2018`
`A=2018/2018-1/2018`
`A=2017/2018`
Vậy `A=2017/2018`
Bài 5:
`E=(x-5)/(x+2)` `(x in ZZ ;x != -2)`
`E=(x+2-7)/(x+2)`
`E=(x+2)/(x+2)-7/(x+2)`
`E=1-7/(x+2)`
Để `E` nguyên thì `(-7)/(x+2)` phải nguyên.
`(-7)/(x+2)` nguyên khi `-7vdotsx+2`
`⇒x+2 in Ư(-7)={+-1;+-7}`
Ta có bảng:
Vậy nếu `x in {-9;-3;-1;5}` thì `E` nguyên.