Question

x/x-a +x/x-b =2 ,find x

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Answer 1

that's the solution ,I hope u will be getting help from me

Answer 2

The value of x is $x=\frac{2ab}{a+b};\quad \:a\ne \:-b$

Step-by-step explanation:

The given equation is

$\frac{x}{x-a}+\frac{x}{x-b}=2$

The LCM is (x-a)(x-b). So, multiply both sides by (x-a)(x-b)

$\frac{x}{x-a}\left(x-a\right)\left(x-b\right)+\frac{x}{x-b}\left(x-a\right)\left(x-b\right)=2\left(x-a\right)\left(x-b\right)$

On simplifying, we get

$x\left(x-b\right)+x\left(x-a\right)=2\left(x-a\right)\left(x-b\right)\\\\2x^2-ax-bx=2\left(x^2-bx-ax+ab\right)\\\\2x^2-ax-bx=2x^2-2bx-2ax+2ab$

Subtract $2x^2-2bx-2ax$ to both sides

$2x^2-ax-bx-\left(2x^2-2bx-2ax\right)=2x^2-2bx-2ax+2ab-\left(2x^2-2bx-2ax\right)\\\\ax+bx=2ab$

Factor out x from left hand side

$x\left(a+b\right)=2ab$

Divide both sides by (a+b)

$x=\frac{2ab}{a+b};\quad \:a\ne \:-b$

#Learn More:

Simplify:

3y-(4y-(6y+3(5y-x)))​