Question

Express
`(x)/(x+2) +(2x)/(x-4)`as a single fraction in its simplest form.

Answer 1

`(3x^2)/((x+2)(x-4))`

Explanation:

Before adding the fractions we require them to have a common denominator.

Multiply numerator/ denominator of first fraction by x - 4

Multiply numerator/ denominator of second fraction by x + 2

=
`(x(x-4))/((x+2)(x-4))` +
`(2x(x+2))/((x+2)(x-4))` ← expand and simplify numerators, leaving common denominator

=
`(x^2-4x+2x^2+4x)/((x+2)(x-4))`

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