solve 1/( k + 1) + 2/(k)=4/3?

Question

help me solve this one!!!!

Answer 1

1/(k+1) +2/k =4/3
=>{1*k+2(k+1)}/k(k+1)=4/3
=>(k+2k+2)/(k^2+k)=4/3
=>(3k+2)/(K^2+k)=4/3
=>4k^2+4k=9k+6 [by cross multipliation]
=>4k^2+4k-9k-6=0
=> 4k^2-5k-6=0
=>4k^2-8k+3k-6=0
=>4k(k-2)+3(k-2)=0
=>(k-2)(4k+3)=0
therefore,either k-2=0 or 4k+3=0
If k-2=0,then k=2
if 4k+3=0,then k= -3/4
Hence x=2 or -3/4 ans

Answer 2

3k + 6 (k + 1) = 4k.(k + 1)
3k + 6k + 6 = 4k² + 4k
4k² - 5k - 6 = 0
(4k + 3).(k - 2) = 0
k = - 4/3 , k = 2