Need help solving for a variable.

Question

We have: $$\sqrt{k} = \frac{\sqrt{k}}{2} + b$$

We need to solve for b, i have thought long and hard about how to get it to what the answer is $(\sqrt{k}/2)$, but my algebra is garbage. Would like some help on how to solve for b.

Thanks

Answer 1

One simple way to see how to approach this (assuming $k\ne 0$) is to divide both sides by $\sqrt{k}$ which yields $$ 1 = \frac{1}{2} + \frac{b}{\sqrt{k}}, $$ therefore, $$ \frac{1}{2} = \frac{b}{\sqrt{k}}. $$ Can you finish this?

Answer 2

Honestly I'm unsure if this is a troll question but in any case:

$\sqrt{k} = \frac{\sqrt{k}}{2} + b$

Subtract $\frac{\sqrt{k}}{2}$ from both sides so you get $\sqrt{k} - \frac{\sqrt{k}}{2} = b$

So that is $\frac{2\sqrt{k}}{2}-\frac{\sqrt{k}}{2} = \frac{\sqrt{k}}{2}$

(I just added two fractions in the last step, got the common denominator, etc.)