Question

How to subtract algebraic fractions

Answer 1

`(5x+16)/((x+4)(x+6))`

Explanation:

Before subtracting we require the fractions to have a common denominator.

The lowest common multiple of x + 4 and x + 6 is (x + 4)(x + 6)

Multiply the numerator/denominator of the first fraction by x + 6 and

multiply the numerator/denominator of the second fraction by x + 4

=
`((x+2)(x+6))/((x+4)(x+6))` -
`((x-1)(x+4))/((x+4)(x+6))`

Expand the numerators and simplify leaving the denominator

=
`(x^2+8x+12-(x^2+3x-4))/((x+4)(x+6))`

=
`(x^2+8x+12-x^2-3x+4)/((x+4)(x+6))`

=
`(5x+16)/((x+4)(x+6))`