+0  
 
0
790
2
avatar+646 

(1/a) - (1/b) = (1/c) 

make a the subject

 Feb 26, 2018
 #1
avatar
0

Solve for a:

1/a - 1/b = 1/c

 

Bring 1/a - 1/b together using the common denominator a b:

(b - a)/(a b) = 1/c

 

Cross multiply:

c (b - a) = a b

 

Expand out terms of the left hand side:

b c - a c = a b

 

Subtract a b + b c from both sides:

a (-b - c) = -b c

 

Divide both sides by -b - c:

a = (bc) / (b + c)

 Feb 26, 2018
 #2
avatar+20850 
0

(1/a) - (1/b) = (1/c) 

make a the subject

 

\(\begin{array}{|rcll|} \hline \dfrac{1}{a}-\dfrac{1}{b} &=& \dfrac{1}{c} \quad & | \quad +\dfrac{1}{b} \\\\ \dfrac{1}{a} &=& \dfrac{1}{c} +\dfrac{1}{b} \\\\ \dfrac{1}{a} &=& \dfrac{1}{c}\cdot \dfrac{b}{b} +\dfrac{1}{b}\cdot \dfrac{c}{c} \\\\ \dfrac{1}{a} &=& \dfrac{b}{bc} +\dfrac{c}{bc} \\\\ \dfrac{1}{a} &=& \dfrac{b+c}{bc} \\\\ \dfrac{a}{1} &=& \dfrac{bc}{b+c} \\\\ \mathbf{a} & \mathbf{=} & \mathbf{\dfrac{bc}{b+c}} \\\\ \hline \end{array}\)

 

laugh

 Feb 27, 2018

43 Online Users

avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.