# How do you solve (a+3)/a-6/(5a)=1/a?

Apr 12, 2017

color(blue)(a=-4/5

#### Explanation:

$\frac{a + 3}{a} - \frac{6}{5 a} = \frac{1}{a}$

$\therefore \frac{a + 3}{a} - \frac{1}{a} = \frac{6}{5 a}$

$\therefore \frac{a + 3 - 1}{a} = \frac{6}{5 a}$

multiply L.H.S and R.H.S by $5 a$

$\therefore {\left(5 \cancel{a}\right)}^{\textcolor{g r e e n}{1}} / 1 \times \frac{a + 3 - 1}{\cancel{a}} ^ \textcolor{g r e e n}{1} = \frac{6}{\cancel{5 a}} ^ \textcolor{g r e e n}{1} \times {\cancel{5 a}}^{\textcolor{g r e e n}{1}} / 1$

$\therefore 5 \left(a + 3 - 1\right) = 6$

$\therefore 5 \left(a + 2\right) = 6$

$5 a + 10 = 6$

$\therefore 5 a = 6 - 10$

$\therefore 5 a = - 4$

:.color(blue)(a=-4/5

substitute color(blue)(a=-4/5

$\therefore \frac{- \left(\frac{4}{5}\right) + 3}{- \frac{4}{5}} - \frac{6}{5 \left(- \frac{4}{5}\right)} = \frac{1}{- \frac{4}{5}}$

$\therefore \frac{- \frac{4}{5} + \frac{15}{5}}{- \frac{4}{5}} - \frac{6}{- \frac{20}{5}} = 1 \times - \frac{5}{4}$

$\therefore \frac{\frac{11}{5}}{- \frac{4}{5}} - \frac{6}{-} 4 = - \frac{5}{4}$

$\therefore \frac{11}{\cancel{5}} ^ 1 \times - {\cancel{5}}^{1} / 4 = - \frac{5}{4}$

$\therefore \frac{11}{-} 4 - \frac{6}{-} 4 = - \frac{5}{4}$

:.color(blue)(5/-4=5/-4