`(x+1)/(x+6)+1/x=(2x+1)/(x+6)` Solve the equation by using the LCD. Check for extraneous solutions.

Expert Answers

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LCD is `x(x+6)`

Multiply all the terms of the equation by LCD and simplify,







Factorize the above equation,





use the zero product property,

`x+2=0`  or `x-3=0`

`x=-2`   or `x=3`

Let's check the solutions by plugging them in the original equation,

For x=-2,




It's true.

For x=3,




It's true.

So, the solutions of the equation are 3 and -2.

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