# Question #acd2f

Jul 31, 2017

$b = \frac{2}{c} + a$

#### Explanation:

Given: $\frac{a}{c} = \left(b - a\right) \frac{a}{2}$

Multiply both sides by $\frac{2}{a}$:

$\frac{2}{c} = b - a$

Flip the equation:

$b - a = \frac{2}{c}$

$b = \frac{2}{c} + a$

Jul 31, 2017

$\frac{a}{c} = \left(b - a\right) \frac{a}{2}$

$\implies b = \frac{2}{c} + a$

#### Explanation:

We need to isolate $b$ in the formula

$\frac{a}{c} = \left(b - a\right) \frac{a}{2}$

$\iff$ Distribute

$\frac{a}{c} = \frac{b a}{2} - {a}^{2} / 2$

$\iff$ Add ${a}^{2} / 2$ to both sides

$\frac{a}{c} + {a}^{2} / 2 = \frac{b a}{2}$

$\iff$ Find a common denominator

$\frac{2 a + {a}^{2} c}{2 c} = \frac{b a}{2}$

$\iff$ Multiply both sides by $2$

$\frac{2 a + {a}^{2} c}{c} = b a$

$\iff$ Divide both sides by $a$

$\frac{2 a + {a}^{2} c}{a c} = b$

$\iff$ Simplify

$\frac{2 + a c}{c} = b$

$\iff$ Simplify
$\frac{2}{c} + a = b$