Question

solve the equation 1/x+3-1/x-6=9/20

Answer 1

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Answer 2

Answer:

The solution of the equation is at x=1 and 2.

Step-by-step explanation:

Given : Equation $\frac{1}{x+3}-\frac{1}{x-6} =\frac{9}{20}$

To find : The solution of the equation?

Solution :

We solve the given equation by taking LCM of the denominator.

$\frac{1}{x+3}-\frac{1}{x-6} =\frac{9}{20}$

$\frac{x-6-(x+3)}{(x+3)(x-6)}=\frac{9}{20}$

$\frac{x-6-x-3)}{x^2-6x+3x-18}=\frac{9}{20}$

$\frac{-9}{x^2-3x-18}=\frac{9}{20}$

Cross multiply,

$x^2-3x-18=\frac{-9\times 20}{9}$

$x^2-3x-18=-20$

$x^2-3x+2=0$

Solve by middle term split,

$x^2-2x-x+2=0$

$x(x-2)-1(x-2)=0$

$(x-2)(x-1)=0$

$x=1,2$

Therefore, The solution of the equation is at x=1 and 2.