Question

I need help with these. I will fan and medal

1) 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

cross multiple

Answer 2

multiply each term by 4x ( the LCD) is another way to do this

Answer 3

There are two strategies. one way is to add the fractions on the left using a common denominator of 2x

The other way is to "clear the denominators" which is a fancy way to say
"multiply the equation by the common denominator of all the terms"
in this case 4x

you would get this:
\[ 4x\left( \frac{1}{2} + \frac{3}{x}= \frac{3}{4}\right)\\
\frac{1\cdot 4x}{2} + \frac{3\cdot 4x}{x}= \frac{3\cdot 4x}{4}

\] and if you simplify each term you get
\[ 2x +12= 3x \]
now add -2x to both sides
\[ 12=x \]

Answer 4

-1/2+1/2+3/x = 3/4-1/2 [add both sides -1/2]
3/x = 3/4 - 2/4 [ here i write 1/2 = 2/4]

3/x = 1/4

x/3 = 4/1

multiply both sides with 3
x = 12

Answer 5

I got this completely wrong earlier. I don't know what I was thinking. Sorry if I confused you! The above answers are correct.

Answer 6

This is hard, You sure?