The solution
Explanation:Given:
[tex]\frac{2}{x}\text{ + 3 = }\frac{14}{x}[/tex]To find:
to solve the rational expression
[tex]\begin{gathered} LCMof\text{ the left side = x} \\ \frac{2+3x}{x}\text{ = }\frac{14}{x} \\ \\ cross\text{ multiply:} \\ x(2\text{ + 3x\rparen = x \lparen14\rparen} \end{gathered}[/tex][tex]\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}[/tex]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
[tex]\begin{gathered} when\text{ x = 4} \\ left\text{ side = }\frac{2}{4}\text{ + 3} \\ =3\frac{2}{4}=\text{ 3}\frac{1}{2} \\ \\ right\text{ side = }\frac{14}{4} \\ =\text{ 3}\frac{2}{4} \\ =\text{ 3}\frac{1}{2} \end{gathered}[/tex]The solution set is (4, 3 1/2)