Question

If $y = \frac{ax^2}{(x-a)(x-b)(x-c)}+\frac{bx}{((x-b)(x-c)}+\frac{c}{x-c}+1,$ prove that $\frac{y'}{y} = \frac{1}{x}\bigg \lgroup \frac{a}{a-x}+\frac{b}{b-x}+\frac{c}{c-x}\bigg \rgroup .$

Answer 1

If $y = \frac{ax^2}{(x-a)(x-b)(x-c)}+\frac{bx}{((x-b)(x-c)}+\frac{c}{x-c}+1,$ prove that $\frac{y'}{y} = \frac{1}{x}\bigg \lgroup \frac{a}{a-x}+\frac{b}{b-x}+\frac{c}{c-x}\bigg \rgroup .$