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

Answer:

we are given a variable equation as:

$\dfrac{1}{2}+\dfrac{3}{x}=\dfrac{3}{4}$

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

$\dfrac{3}{x}=\dfrac{3}{4}-\dfrac{1}{2} \\\\\dfrac{3}{x}=\dfrac{3-1\times 2}{4}\\\\\dfrac{3}{x}=\dfrac{3-2}{4}\\\\\dfrac{3}{x}=\dfrac{1}{4}\\\\x=12$

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