Question

How do you solve $\dfrac{1}{8}+\dfrac{2}{t}=\dfrac{17}{8t}$?

Answer 1

Hint:For solving the given equation, we first need to separate the variables on one side of the equation. For this, we need to subtract \[\dfrac{2}{t}\] from both the sides of the given equation to get \[\dfrac{17}{8t}-\dfrac{2}{t}=\dfrac{1}{8}\]. Then we need to take the LCM on the LHS to simplify the equation as $\dfrac{1}{8t}=\dfrac{1}{8}$. Finally, on taking the reciprocals of both the sides, we will obtain the required solution of the given equation.

Complete step-by-step answer:
The equation given in the above question is
\[\Rightarrow \dfrac{1}{8}+\dfrac{2}{t}=\dfrac{17}{8t}\]
Subtracting \[\dfrac{2}{t}\] from both the sides, we get
\[\begin{align}
  & \Rightarrow \dfrac{1}{8}+\dfrac{2}{t}-\dfrac{2}{t}=\dfrac{17}{8t}-\dfrac{2}{t} \\
 & \Rightarrow \dfrac{1}{8}=\dfrac{17}{8t}-\dfrac{2}{t} \\
 & \Rightarrow \dfrac{17}{8t}-\dfrac{2}{t}=\dfrac{1}{8} \\
\end{align}\]
Taking the LCM on the LHS of the above equation, we get
$\begin{align}
  & \Rightarrow \dfrac{17-2\times 8}{8t}=\dfrac{1}{8} \\
 & \Rightarrow \dfrac{17-16}{8t}=\dfrac{1}{8} \\
 & \Rightarrow \dfrac{1}{8t}=\dfrac{1}{8} \\
\end{align}$
Taking the reciprocals on both the sides of the above equation, we get
$\Rightarrow 8t=8$
Finally, on dividing the above equation by $8$, we get
$\begin{align}
  & \Rightarrow \dfrac{8t}{8}=\dfrac{8}{8} \\
 & \Rightarrow t=1 \\
\end{align}$
Hence, the solution of the given equation is $t=1$.

Note: As can be seen in the above solution that there are many calculations involved. Therefore, there may be calculation errors too. So we must check the final obtained solution by back substituting it into the given equation. If the LHS comes equal to RHS, then the solution is correct. But if they not coming equal, then it means that there is error in the solution. For example, on substituting the obtained solution $t=1$ into the LHS of the given equation, we get $\dfrac{1}{8}+\dfrac{2}{1}=\dfrac{1+16}{8}=\dfrac{17}{8}$. And then on putting $t=1$ into the RHS of the given equation, we get $\dfrac{17}{8\left( 1 \right)}=\dfrac{17}{8}$. Since both the LHS and the RHS are equal to $\dfrac{17}{8}$, our obtained solution is correct.