# If (a+1)/(b-1)=5/1 and (a-1)/(b+1)=1/1, how do you find the value of b/a?

Mar 27, 2018

$\frac{b}{a} = \frac{1}{2}$

#### Explanation:

We can see that

$a + 1 = 5 \left(b - 1\right)$

$a + 1 = 5 b - 5$

$6 = 5 b - a$

And

$a - 1 = b + 1$

$a - 2 = b$

Substituting the second equation into the first we get

$6 = 5 \left(a - 2\right) - a$

$6 = 5 a - 10 - a$

$16 = 4 a$

$a = 4$

It follows that $b = 4 - 2 = 2$ .

Therefore $\frac{b}{a} = \frac{2}{4} = \frac{1}{2}$

Hopefully this helps!