Solve the following for x-1-2 a-b-2 x-1-2 a-1-5-1-2 x

The given equation is 1/2a + b + 2x = 1/2a + 1/b + 1/2x 1/2a + b + 2x = 1/2a + 1/b + 1/2x ⇒1/2a + b + 2x 1/2x = 1/2a + 1/b ⇒2x 2a b 2x/2x (2a + b + 2x) ...

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Standard X

Mathematics

Quadratic Formula

Solve the fol...

Question

Solve the following for x :
$\frac{1}{2 a + b + 2 x} = \frac{1}{2 a} + \frac{1}{b} + \frac{1}{2 x}$

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Solution

The given equation is $\frac{1}{2 a + b + 2 x} = \frac{1}{2 a} + \frac{1}{b} + \frac{1}{2 x}$
$\frac{1}{2 a + b + 2 x} = \frac{1}{2 a} + \frac{1}{b} + \frac{1}{2 x} \Rightarrow \frac{1}{2 a + b + 2 x} - \frac{1}{2 x} = \frac{1}{2 a} + \frac{1}{b} \Rightarrow \frac{2 x - 2 a - b - 2 x}{2 x (2 a + b + 2 x)} = \frac{b + 2 a}{2 a b} \Rightarrow \frac{- 2 a - b}{2 x (2 a + b + 2 x)} = \frac{b + 2 a}{2 a b} \Rightarrow \frac{- (2 a + b)}{2 x (2 a + b + 2 x)} = \frac{b + 2 a}{2 a b} \Rightarrow \frac{- 1}{x (2 a + b + 2 x)} = \frac{1}{a b} \Rightarrow 2 x^{2} + 2 a x + b x + a b = 0 \Rightarrow 2 x (x + a) + b (x + a) = 0 \Rightarrow (x + a) (2 x + b) = 0 \Rightarrow x + a = 0 o r 2 x + b = 0 \Rightarrow x = - a, o r x = \frac{- b}{2}$

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Solve for $x : \frac{1}{2 a + b + 2 x} = \frac{1}{2 a} + \frac{1}{b} + \frac{1}{2 x}$

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Solve the following for x : 12a+b+2x=12a+1b+12x

The given equation is 12a+b+2x=12a+1b+12x 12a+b+2x=12a+1b+12x⇒12a+b+2x−12x=12a+1b⇒2x−2a−b−2x2x(2a+b+2x)=b+2a2ab⇒−2a−b2x(2a+b+2x)=b+2a2ab⇒−(2a+b)2x(2a+b+2x)=b+2a2ab⇒−1x(2a+b+2x)=1ab⇒2x2+2ax+bx+ab=0⇒2x(x+a)+b(x+a)=0⇒(x+a)(2x+b)=0⇒x+a=0or2x+b=0⇒x=−a, or x=−b2

Solve the following for x :
$\frac{1}{2 a + b + 2 x} = \frac{1}{2 a} + \frac{1}{b} + \frac{1}{2 x}$