Identify the value of x in the equation x-x-a-x-x-b-2-A- abB- a-bC- 2 a b-a-bD- 2 ab

The correct option is C 2ab/a+b x/x a+x/x b=2 x(x b)+x(x a)/(x a)(x b)=2 x^2 xb+x^2 xa=2[(x b)(x a)] 2x^2 xb xa=2[x^2 xb ax+ab] 2x^2 xb xa=2x^2 2xb 2ax+2ab Can ...

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Byju's Answer

Standard VII

Mathematics

Solving Equations with Variable on Both Sides

Identify the ...

Question

Identify the value of x in the equation $\frac{x}{x - a} + \frac{x}{x - b} = 2$ .

$\frac{a}{b}$

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$a b$

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$\frac{2 a b}{a + b}$

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$2 a b$

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Solution

The correct option is C
$\frac{2 a b}{a + b}$

$\frac{x}{x - a} + \frac{x}{x - b} = 2$
$\frac{x (x - b) + x (x - a)}{(x - a) (x - b)} = 2$
$x^{2} - x b + x^{2} - x a = 2 [(x - b) (x - a)]$
$2 x^{2} - x b - x a = 2 [x^{2} - x b - a x + a b]$
$2 x^{2} - x b - x a = 2 x^{2} - 2 x b - 2 a x + 2 a b$
Cancelling similar terms on both sides,
$- x b - x a = - 2 x b - 2 a x + 2 a b$
Shifting all $x$ terms to LHS.
$x b + a x = 2 a b$
$x (a + b) = 2 a b$
$x = \frac{2 a b}{a + b}$ .

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