## Algebra: A Combined Approach (4th Edition)

$\frac{a}{a - 3}$ = $\frac{3}{a - 3}$ - $\frac{3}{2}$ Subtracting $\frac{3}{a - 3}$ from both sides, we get $\frac{a}{a - 3}$ - $\frac{3}{a - 3}$ = $\frac{3}{a - 3}$ - $\frac{3}{2}$ - $\frac{3}{a - 3}$. On the left hand side, the denominators are equal, and thus we can directly subtract the numerators. Thus, $\frac{a - 3}{a - 3}$ = -$\frac{3}{2}$ ...(Since $\frac{3}{a - 3}$ - $\frac{3}{a - 3}$ = 0). $\frac{a - 3}{a - 3}$ = -$\frac{3}{2}$ But, $\frac{a - 3}{a - 3}$ = 1, and 1 $\ne$ -$\frac{3}{2}$. Thus this equation has no solution.