Page:Elementary algebra (1896).djvu/143

Rh violating cyclic order by the use of arrangements such as $$b - c$$, $$a - c$$, $$a-b$$, or $$a - c$$, $$b - a$$, $$b - c$$. It will always be found that the work is rendered shorter and easier by following cyclic order from the beginning, and adhering to it throughout the question.

Find the value of


 * 1) $$ \frac{a}{\left ( a-b \right ) \left ( a-c \right ) } + \frac{b}{\left ( b-c \right ) \left ( c-a \right ) } + \frac{c}{\left ( c-a \right ) \left ( c-b \right ) } $$
 * 2) $$ \frac{b}{\left ( a-b \right ) \left ( a-c \right ) } + \frac{c}{\left ( b-c \right ) \left ( c-a \right ) } + \frac{a}{\left ( c-a \right ) \left ( c-b \right ) } $$
 * 3) $$ \frac{z}{\left ( x-y \right ) \left ( x-z \right ) } + \frac{x}{\left ( y-z \right ) \left ( z-y \right ) } + \frac{y}{\left ( z-x \right ) \left ( z-y \right ) } $$
 * 4) $$ \frac{y+z}{\left ( x-y \right ) \left ( x-z \right ) } + \frac{z+x}{\left ( y-z \right ) \left ( y-z \right ) } + \frac{x+y}{\left ( z-x \right ) \left ( z-y \right ) } $$
 * 5) $$ \frac{b-c}{\left ( a-b \right ) \left ( a-c \right ) } + \frac{c-a}{\left ( b-c \right ) \left ( b-a \right ) } + \frac{a-b}{\left ( c-a \right ) \left ( c-b \right ) } $$
 * 6) $$ \frac{x^2yz}{\left ( x-y \right ) \left ( x-z \right ) } + \frac{y^2zx}{\left ( y-z \right ) \left ( y-x \right ) } + \frac{z^2xy}{\left ( z-x \right ) \left ( z-y \right ) } $$
 * 7) $$ \frac{x^2yz}{\left ( x-y \right ) \left ( x-z \right ) } + \frac{y^2zx}{\left ( y-z \right ) \left ( y-x \right ) } + \frac{z^2xy}{\left ( z-x \right ) \left ( z-y \right ) } $$
 * 8) $$ \frac{p-a}{\left ( p-q \right ) \left ( p-r \right ) } + \frac{q-a}{\left ( q-r \right ) \left ( q-p \right ) } + \frac{r-a}{\left ( r-p \right ) \left ( r-q \right ) } $$
 * 9) $$ \frac{p+q-r}{\left ( p-q \right ) \left ( p-r \right ) } + \frac{q+r-p}{\left ( q-r \right ) \left ( q-p \right ) } + \frac{r+p-q}{\left ( r-p \right ) \left ( r-q \right ) } $$
 * 10) $$ \frac{a^2}{\left ( a^2-b^2 \right ) \left ( a^2-c^2 \right ) } + \frac{b^2}{\left ( b^2-c^2 \right ) \left ( b^2 - a^2 \right ) } + \frac{c2}{\left ( c^2-a^2 \right ) \left ( c^2-b^2 \right ) } $$
 * 11) $$ \frac{x+y}{\left ( p-q \right ) \left ( p-r \right ) } + \frac{x+y}{\left ( q-r \right ) \left ( q - p \right ) } + \frac{x+y}{\left ( r-p \right ) \left ( r-q \right ) } $$
 * 12) $$ \frac{q+r}{\left ( x-y \right ) \left ( x-z \right ) } + \frac{r+p}{\left ( y-z \right ) \left ( y - x \right ) } + \frac{p+q}{\left ( z-x \right ) \left ( z-y \right ) } $$