Question

If the two expressions are equivalent, find value of x

Answer 1

`(5)/(x)-(1)/(3)=(1)/(x)`

1. Subtract 1/x in both sides of the equation:

`\begin{gathered} (5)/(x)-(1)/(x)-(1)/(3)=(1)/(x)-(1)/(x) \\ \\ (4)/(x)-(1)/(3)=0 \end{gathered}`

2. Add 1/3 in both sides of the equation:

`\begin{gathered} (4)/(x)-(1)/(3)+(1)/(3)=0+(1)/(3) \\ \\ (4)/(x)=(1)/(3) \end{gathered}`

3. Multiply both sides of the equation by x:

`\begin{gathered} x\cdot(4)/(x)=x\cdot(1)/(3) \\ \\ 4=(x)/(3) \end{gathered}`

4. Multiply both sides of the equation by 3:

`\begin{gathered} 4\cdot3=(x)/(3)\cdot3 \\ \\ 12=x \\ \\ \text{ Rewrite} \\ x=12 \end{gathered}`Then, the value of x is 12