ex1.6_10

Example

$v$ $\quad \displaystyle v + \frac{2}{v} = 8 -\frac{13}{v}$

Solution

Since this equation does not set a single fraction equal to another single fraction, it cannot be solved by cross multiplying. Instead we clear fractions.

The denominators of the individual fractions are

1, \, v, \, 1, \, \mbox{and} \, v,

$v$ $v$ will clear fractions.

v \left( v + \frac{2}{v} \right) = v \left( 8 -\frac{13}{v}\right)\\[0.25 in] v^2+2 = 8v-13\\[0.25 in] v^2 -8v +15 = 0\\[0.25 in] (v-3)(v-5)=0\\[0.25 in] v=3 \quad \mbox{or} \quad v=5

$v=3$ $v=5$ .