Question

metal and fan

George tells you that when variables are in the denominator, the equation four over five plus three over x equals one over two becomes unsolvable. George explains, "There is a value for x that makes the denominator zero, and you can't divide by zero." Demonstrate to George how the equation is still solvable and explain your reasoning.

Answer 1

\[\frac{ 4 }{ 5 }+\frac{ 3 }{ x }=\frac{ 1 }{ 2 }\]
restriction is \[x \neq 0\]
\[\frac{ 3 }{ x }=\frac{ 1 }{ 2 }-\frac{ 4 }{ 5 }\]
\[\frac{ 3 }{ x }=\frac{ 5-8 }{ 10 }=-\frac{ 3 }{ 10 }\]

Answer 2

\[\frac{ x }{ 3 }=-\frac{ 10 }{ 3 }\]
x=?