7 Let Ht t1t2t Write H as a quotient H fg and as a produc

7. Let H(t) = (t+1)/(t^2-t) . Write H as a quotient H = f/g and as a product H = hk, where f,g,h, and k are four distinct functions.

t +1 ,2-7. Write H as a quotient H--and as a product H-hk, where 7. Let H (t) = ,g, h, k are four distinct functions.

Solution

H(t) = (t + 1)/(t² - t)

H = f/g ==> f = (t + 1) ; g = (t² - t)

H = (t + 1)/(t² - t)

==> H = (t + 1)/[t(t - 1)]

==> H = (1/t) * [(t + 1)/(t - 1)] = hk

==> h = 1/t ; k = (t + 1)/(t - 1)