Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I know this might seem very simple, but I can't seem to isolate x.

$$\frac{1}{x} = \frac{1}{a} + \frac{1}{b} $$

Please show me the steps to solving it.

share|improve this question

3 Answers 3

up vote 1 down vote accepted

You should combine $\frac1a$ and $\frac1b$ into a single fraction using a common denominator as usual:

$$\begin{eqnarray} \frac1x& = &\frac1a + \frac1b \\ &=&{b\over ab} + {a\over ab} \\ &=& b+a\over ab \end{eqnarray}$$

So we get: $$x = {ab\over{b+a}}.$$

Okay?

share|improve this answer
    
and x~=0. Correct ! –  Zeta.Investigator Aug 20 '12 at 17:31
    
How exactly did you flip ${1\over{x}} = {b + a\over{ab}}$ to $x = {ab\over{b+a}}$ ? –  Dan the Man Aug 20 '12 at 17:34
    
@Dan: Suppose that $\frac{u}v=\frac{x}y$. Multiply through by $vy$ to get $uy=xv$, then divide through by $ux$ to get $\frac{y}x=\frac{v}u$. Alternatively, multiply both sides of the original equation by $\frac{y}x$ t0 get $\frac{uy}{vx}=1$, then multiply both sides of that equation by $\frac{v}u$ to get $\frac{y}x=\frac{v}u$. Whenever two non-zero fractions are equal, their reciprocals (obtained by turning them upside down) are also equal. –  Brian M. Scott Aug 20 '12 at 17:41
    
Awesome. Thank you. –  Dan the Man Aug 20 '12 at 17:43

$\frac{1}{x} = \frac{b}{ab} + \frac{a}{ab}$

$\frac{1}{x} = \frac{a + b}{ab}$

$x = \frac{ab}{a + b}$

note that $\frac{1}{x} = \frac{1}{a} + \frac{1}{b}$ is possible if and only if $\frac{1}{a} + \frac{1}{b} \neq 0$. This implies that $a \neq -b$; and, hence $a + b \neq 0$.

share|improve this answer

1/x = (a+b)/ab , x~=0
x=ab/(a+b),x~=0

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.