Solve for X 1 - 2 a-b-2 x-1 - 2 a-1 - b-1 - 2 x

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) = (2a + b) / 2ab (2a + b) / (2x)(2a+b+2x) = ...

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Byju's Answer

Standard X

Mathematics

Finding Solution for Consistent Pair of Linear Equations

Solve for X 1...

Question

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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Solution

Given: $\frac{1}{2 a + b + 2 x} = \frac{1}{2 a} + \frac{1}{b} + \frac{1}{2 x}$
$\Rightarrow \frac{1}{2 a + b + 2 x} - \frac{1}{2 x} = \frac{1}{2 a} + \frac{1}{b}$
$\Rightarrow \frac{2 x - 2 a - b - 2 x}{(2 a + b + 2 x) (2 x)} = \frac{2 a + b}{2 a b}$
$\Rightarrow \frac{- (2 a + b)}{4 a x + 2 b x + 4 x^{2}} = \frac{2 a + b}{2 a b}$
$\Rightarrow \frac{- 1}{4 a x + 2 b x + 4 x^{2}} = \frac{1}{2 a b}$
$\Rightarrow 4 a x + 2 b x + 4 x^{2} = - 2 a b$
$\Rightarrow 4 a x + 2 b x + 4 x^{2} + 2 a b = 0$
$\Rightarrow 4 a x + 4 x^{2} + 2 b x + 2 a b = 0$
$\Rightarrow 4 x (a + x) + 2 b (x + a) = 0$
$\Rightarrow (4 x + 2 b) (a + x) = 0$
$\Rightarrow x = \frac{- 2 b}{4}$ or $x = - a$
$∴ x = \frac{- b}{2}, - a$

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Solve for x:12a+b+2x=12a+1b+12x ​​​​​​ ​​​​​​

Given: 12a+b+2x=12a+1b+12x⇒12a+b+2x−12x=12a+1b⇒2x−2a−b−2x(2a+b+2x)(2x)=2a+b2ab⇒−(2a+b)4ax+2bx+4x2=2a+b2ab⇒−14ax+2bx+4x2=12ab⇒4ax+2bx+4x2=−2ab⇒4ax+2bx+4x2+2ab=0⇒4ax+4x2+2bx+2ab=0⇒4x(a+x)+2b(x+a)=0⇒(4x+2b)(a+x)=0⇒x=−2b4 or x=−a∴x=−b2,−a

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