# How do you solve a-5/a=4?

Dec 22, 2016

$a = 5$

#### Explanation:

$a - \frac{5}{a} = 4$

multiply by $a$:

${a}^{2} - 5 = 4 a$

add $5$:

${a}^{2} = 4 a + 5$

${a}^{2} > 4 a$

$a > 4$

trial:
$a = 5$

${a}^{2} = 4 a + 5$

$= 20 + 5 = 25$

${a}^{2} = 25$

$a = 5$

Dec 26, 2016

$a = 5 \text{ or } a = - 1$

#### Explanation:

$a - \frac{5}{a} = 4 \text{ } \leftarrow$ we can see $a \ne 0$

Multiply by $a$ to get rid of the fraction.

${a}^{2} - 5 = 4 a \text{ } \leftarrow$ a quadratic, make it equal to 0

${a}^{2} - 4 a - 5 = 0 \text{ } \leftarrow$ factorise

$\left(a - 5\right) \left(a + 1\right) = 0 \text{ } \leftarrow$ either factor can be =0

If $a - 5 = 0 , \text{ then } a = 5$

If $a + 1 = 0 , \text{ then } a = - 1$