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

Mar 31, 2017

$t = \pm \frac{\sqrt{6}}{2} \approx 1.2247 \ldots$

#### Explanation:

$\textcolor{g r e e n}{\left[\frac{2 t}{t + 1}\right] + \left[\textcolor{w h i t e}{.} 4 \left(t - 1\right) \textcolor{red}{\times 1} \textcolor{w h i t e}{.}\right] \text{ "=" } \left[\textcolor{w h i t e}{.} 2 \textcolor{red}{\times 1} \textcolor{w h i t e}{.}\right]}$

$\textcolor{g r e e n}{\left[\frac{2 t}{t + 1}\right] + \left[\textcolor{w h i t e}{.} 4 \left(t - 1\right) \textcolor{red}{\times \frac{t + 1}{t + 1}} \textcolor{w h i t e}{.}\right] \text{ "=" } \left[\textcolor{w h i t e}{.} 2 \textcolor{red}{\times \frac{t + 1}{t + 1}} \textcolor{w h i t e}{.}\right]}$

$\frac{2 t}{t + 1} + \frac{4 \left({t}^{2} - 1\right)}{t + 1} \text{ "=" } \frac{2 \left(t + 1\right)}{t + 1}$

Multiply both sides by $\left(t + 1\right)$

$2 t + 4 {t}^{2} - 4 = 2 t + 2$

Divide both sides by 2

$\cancel{\textcolor{w h i t e}{.} t \textcolor{w h i t e}{.}} + 2 {t}^{2} - 2 = \cancel{\textcolor{w h i t e}{.} t \textcolor{w h i t e}{.}} + 1$

$2 {t}^{2} = 3$

${t}^{2} = \frac{3}{2}$

$t = \pm \frac{\sqrt{3}}{\sqrt{2}} \approx 1.2247 \ldots$

$t = \pm \frac{\sqrt{6}}{2} \approx 1.2247 \ldots$