Question

How do you subtract `(3x+1)/(2x) - (x+1)/(x-3)`?

Answer 1

`(x^2-10x-3)/(2x(x-3))`

Explanation:

Before we can subtract the fractions we require them to have a `color(blue)"common denominator"`

To obtain this.

`"multiply numerator/denominator of " (3x+1)/(2x)" by " (x-3)`

`"multiply numerator/denominator of " (x+1)/(x-3)" by " 2x`

`rArr((3x+1)(color(red)(x-3)))/(2x(color(red)(x-3)))-(color(magenta)(2x)(x+1))/(color(magenta)(2x)(x-3))`

The fractions now have a common denominator so we can subtract the numerators while leaving the denominator.

`=((3x+1)(x-3)-2x(x+1))/(2x(x-3))`

distributing the numerator and simplifying gives.

`=(3x^2-8x-3-2x^2-2x)/(2x(x-3))`

`=(x^2-10x-3)/(2x(x-3))`