# How do you solve (7a)/(3a+3)-5/(4a-4)=(3a)/(2a+2)?

Mar 7, 2018

Solution : $a = 3 \mathmr{and} a = - 0.5$

#### Explanation:

$\frac{7 a}{3 a + 3} - \frac{5}{4 a - 4} = \frac{3 a}{2 a + 2}$ or

$\frac{7 a}{3 \left(a + 1\right)} - \frac{5}{4 \left(a - 1\right)} = \frac{3 a}{2 \left(a + 1\right)}$ or

$\frac{7 a}{3 \left(a + 1\right)} - \frac{3 a}{2 \left(a + 1\right)} = \frac{5}{4 \left(a - 1\right)}$ or

$\frac{14 a - 9 a}{6 \left(a + 1\right)} = \frac{5}{4 \left(a - 1\right)}$ or

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

$\frac{a}{6 \left(a + 1\right)} = \frac{1}{4 \left(a - 1\right)}$ or

$4 {a}^{2} - 4 a = 6 a + 6 \mathmr{and} 4 {a}^{2} - 10 a - 6 = 0$ or

$2 {a}^{2} - 5 a - 3 = 0 \mathmr{and} 2 {a}^{2} - 6 a + a - 3 = 0$ or

$2 a \left(a - 3\right) + 1 \left(a - 3\right) = 0 \mathmr{and} \left(a - 3\right) \left(2 a + 1\right) = 0$

$\therefore a = 3 \mathmr{and} a = - \frac{1}{2} = - 0.5$

Solution :$a = 3 \mathmr{and} a = - 0.5$ [Ans]