Question

Hence, write as single
frachon in its lowest terms.
2/y-1 - 4/y^2-1

Answer 1

`(2)/(y+1)`

Explanation:

Factorise the denominator of the second fraction

y² - 1 = (y - 1)(y + 1) ← difference of squares

To obtain a common denominator

multiply numerator/ denominator of first fraction by (y + 1)

=
`(2(y+1))/((y-1)(y+1))` -
`(4)/((y-1)(y+1))` ← subtract numerators leaving the common denominator

=
`(2y+2-4)/((y-1)(y+1))`

=
`(2y-2)/((y-1)(y+1))`

=
`(2(y-1))/((y-1)(y+1))` ← cancel common factor (y - 1) on numerator/denominator

=
`(2)/(y+1)`