# How do you solve 1/8+2/t=17/(8t)?

Oct 16, 2015

$t = 1$.

#### Explanation:

First of all, write the left member as

$\frac{1}{8} + \frac{2}{t} = \frac{t + 2 \cdot 8}{8 t} = \frac{t + 16}{8 t}$

(note that $t$ must not be zero, otherwise we would have $0$ at the denominator).

So we have

$\frac{t + 16}{8 t} = \frac{17}{8 t}$

since the denominators are equal, the equation holds if and only if the numerators are equal. This means

$t + 16 = 17$. Solving for $t$, we get $t = 17 - 16 = 1$.

CHECK: for $t = 1$, the equation becomes

$\frac{1}{8} + 2 = \frac{17}{8}$, which is indeed true.