Question

How do you simplify `(3x)/(x^2+3x-10)- (2x)/(x^2+x-6)`?

Answer 1

`(x(x-1))/((x+5)(x-2)(x+3))`

Explanation:

Adding or subtracting of algebraic fractions is a part of Algebra which students find difficult to master. They are done in exactly the same way as arithmetic fractions.

`rarr "find a common denomiator using factors"`
`rarr " make equivalent fractions"`
`rarr " simplify "`

FACTORISE FACTORISE FACTORISE FACTORISE!!!!!

`(3x)/(x^2 +3x-10) - (2x)/(x^2 +2x -6)`

=`(3x)/((x+5)(x-2)) - (2x)/((x+3)(x-2))`

The LCD must have each factor that is in each denominator, without duplicates.

`(3xcolor(red)((x+3)) - 2xcolor(blue)((x+5)))/(color(blue)((x+5))(x-2)color(red)((x+3))`

Each numerator is multiplied by the factor that is missing in its denominator .

Now simplify the numerator

`(3x^2 +9x -2x^2-10x)/((x+5)(x-2)(x+3))`

=`(x^2-x)/((x+5)(x-2)(x+3))`

=`(x(x-1))/((x+5)(x-2)(x+3))`