Question

How do you solve `(2t)/(t+1)+4(t-1)=2`?

Answer 1

`t=+-sqrt(6)/2~~1.2247...`

Explanation:

`color(green)([(2t)/(t+1) ]+[color(white)(.)4(t-1)color(red)(xx1)color(white)(.)]" "=" "[color(white)(.)2color(red)(xx1)color(white)(.)])`

`color(green)([(2t)/(t+1) ]+[color(white)(.)4(t-1)color(red)(xx(t+1)/(t+1))color(white)(.)]" "=" "[color(white)(.)2color(red)(xx(t+1)/(t+1))color(white)(.)])`

`(2t)/(t+1)+ (4(t^2-1))/(t+1)" "=" "(2(t+1))/(t+1)`

Multiply both sides by `(t+1)`

`2t+4t^2-4=2t+2`

Divide both sides by 2

`cancel(color(white)(.)tcolor(white)(.))+2t^2-2=cancel(color(white)(.)tcolor(white)(.))+1`

`2t^2=3`

`t^2=3/2`

`t=+-sqrt(3)/sqrt(2) ~~1.2247...`

`t=+-sqrt(6)/2~~1.2247...`