Question

How do you evaluate `\frac { 2} { r + 4} = \frac { 4} { r }`?

Answer 1

See a solution process below:

Explanation:

Because both sides of the equation and single fractions we can "flip" the fractions giving:

`(r + 4)/2 = r/4`

Next, multiply each side of the equation by `color(red)(4)` to eliminate the fractions while keeping the equation balanced:

`color(red)(4) xx (r + 4)/2 = color(red)(4) xx r/4`

`cancel(color(red)(4))2 xx (r + 4)/color(red)(cancel(color(black)(2))) = cancel(color(red)(4)) xx r/color(red)(cancel(color(black)(4)))`

`2(r + 4) = r`

Then, expand the term on the left side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`(2 xx r) + (2 xx 4) = r`

`2r + 8 = r`

Now, subtract `color(red)(8)` and `color(blue)(r)` from each side of the equation to solve for `r` while keeping the equation balanced:

`-color(blue)(r) + 2r + 8 - color(red)(8) = -color(blue)(r) + r - color(red)(8)`

`-1color(blue)(r) + 2r + 0 = 0 - color(red)(8)`

`(-1 + 2)r = -8`

`1r = -8`

`r = -8`