Question

Solve the following rational equation. If the equation has no solution so state.

Answer 1

Answer:

The solution

Step-by-step explanation:

Given:

`(2)/(x)\text{ + 3 = }(14)/(x)`

To find:

to solve the rational expression

`\begin{gathered} LCMof\text{ the left side = x} \\ (2+3x)/(x)\text{ = }(14)/(x) \\ \\ cross\text{ multiply:} \\ x(2\text{ + 3x\rparen = x \lparen14\rparen} \end{gathered}`
`\begin{gathered} divide\text{ both sides by x:} \\ 2\text{ + 3x = 14} \\ \\ subtract\text{ 2 from both sides:} \\ 2\text{ - 2 + 3x = 14 - 2} \\ \\ 3x\text{ = 12} \\ divide\text{ both sides by 3:} \\ x\text{ = 12/3} \\ x\text{ = 4} \end{gathered}`

The value of x = 4

The value of the function will e gotten when the value of x is substituted in either left or right side

`\begin{gathered} when\text{ x = 4} \\ left\text{ side = }(2)/(4)\text{ + 3} \\ =3(2)/(4)=\text{ 3}(1)/(2) \\ \\ right\text{ side = }(14)/(4) \\ =\text{ 3}(2)/(4) \\ =\text{ 3}(1)/(2) \end{gathered}`

The solution set is (4, 3 1/2)