# How do you solve 1/m=(m-34)/(2m^2)?

Dec 28, 2016

$m = - 34$. See below.

#### Explanation:

Given $\frac{1}{m} = \frac{m - 34}{2 {m}^{2}}$, we can isolate the variable $m$ to determine its value.

Multiply both sides by $\left(2 {m}^{2}\right)$

$\implies \frac{2 {m}^{2}}{m} = m - 34$

On the left we have ${m}^{2} / {m}^{1}$, which, by the rules of exponents, is equivalent to ${m}^{2 - 1} = {m}^{1} = m$.

$\implies 2 m = m - 34$

Subtract $m$ from both sides

$\implies 2 m - m = - 34$

$\implies m = - 34$

Check your answer by plugging in $- 34$ for $m$ and verifying that the expression is true:

1/(-34)=(-34-34)/(2*(-34)^2

$\implies - \frac{1}{34} = \frac{- 68}{2312}$

Simplify the fraction on the right by dividing numerator and denominator by $68$

$\implies - \frac{1}{34} = - \frac{1}{34}$