Question

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

Answer 1

Answer:

$\frac{2}{y+1}$

Step-by-step 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)

= $\frac{2(y+1)}{(y-1)(y+1)}$ - $\frac{4}{(y-1)(y+1)}$ ← subtract numerators leaving the common denominator

= $\frac{2y+2-4}{(y-1)(y+1)}$

= $\frac{2y-2}{(y-1)(y+1)}$

= $\frac{2(y-1)}{(y-1)(y+1)}$ ← cancel common factor (y - 1) on numerator/denominator

= $\frac{2}{y+1}$