Question

Cindy claims that if there is a variable is in the denominator, the equation three over x plus one over three equals five over six becomes unsolvable. Cindy explains, "There is a value for x that makes the denominator zero, and you can't divide by zero." Demonstrate to Cindy how the equation is still solvable and show all work for full credit.

Answer 1

x = 6

given $\frac{3}{x}$ + $\frac{1}{3}$ = $\frac{5}{6}$

to eliminate the fractions multiply through by the lowest common multiple of x, 3 and 6 , that is 6x

multiply all terms by 6x gives

18 + 2x = 5x ( subtract 2x from both sides )

18 = 3x ( divide both sides by 3 )

6 = x

As a check

$\frac{3}{6}$ + $\frac{1}{3}$ = $\frac{3}{6}$ + $\frac{2}{6}$ = $\frac{5}{6}$