Question

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

Answer 1

`(x^2-x+9)/((x-3)(x+2))`

Explanation:

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

To obtain a common denominator for both fractions.

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

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

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

Now there is a common denominator, subtract the numerators leaving the denominator as it is.

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

distribute the numerator and simplify.

`=(x^2+2x-3x+9)/((x-3)(x+2))`

`=(x^2-x+9)/((x-3)(x+2))`