Question

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

Answer 1

1/2 + 3/x = 3/4
3/x = 3/4 - 1/2
3/x = 3/4 - 2/4
3/x = 1/4....this is a proportion, so we cross multiply
(1)(x) = (3)(4)
x = 12

check..
1/2 + 3/12 = 3/4
6/12 + 3/12 = 3/4
9/12 = 3/4
3/4 = 3/4 (correct)

so x = 12

Answer 2

we are given a variable equation as:

`(1)/(2)+(3)/(x)=(3)/(4)`

we can take variable on one side and constant terms on the other to get

`(3)/(x)=(3)/(4)-(1)/(2) \\\\(3)/(x)=(3-1* 2)/(4)\\\\(3)/(x)=(3-2)/(4)\\\\(3)/(x)=(1)/(4)\\\\x=12`

Hence on solving the following variable equation we get that x=12.