Question

How do you write the mixed expression `(x+7)/(2x)-5x` as a rational expression?

Answer 1

`(-10x^2+x+7)/(2x)`

Explanation:

Multiply by 1 and you do not change the value. However, 1 comes in many forms

Note that `5x" is also " (5x)/1`

`color(green)([(x+7)/(2x)]-[(5x)/1color(red)(xx1)])`

`color(green)([(x+7)/(2x)]-[(5x)/1color(red)(xx(2x)/(2x))])`

`color(green)([(x+7)/(2x)]-[(5xcolor(red)(xx 2x))/color(red)(2x)])`

`color(green)([(x+7)/(2x)]-[(10x^2)/(2x)]`

`color(green)( (-10x^2+x+7)/(2x) )`