Question

PLEASE HELP WITH ALGEBRA!!!

A classmate simplified this rational equation. (Picture attached)


`1 - (2)/(x+3) = (x+1)/(x-3)`

a) circle and explain the error in this simplifcation
b) show your work as you correct the error

Answer 1

Part (a)

The error happens on the 2nd step.

The student multiplied both sides by the LCD (x+3)(x-3) to clear out the fractions, but forgot about the first "1" at the very left.

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Part (b)

`1 - (2)/(x+3) = (x+1)/(x-3)\\\\(x+3)(x-3)*1 - (x+3)(x-3)*(2)/(x+3) = (x+3)(x-3)*(x+1)/(x-3)\\\\(x+3)(x-3) - 2(x-3) = (x+1)(x+3)\\\\x^2-9 - 2x+6 = x^2+4x+3\\\\x^2-2x-3 = x^2+4x+3\\\\x^2-2x-3-x^2-4x-3=0\\\\-6x-6=0\\\\-6x=6\\\\x = 6/(-6)\\\\x = -1`

The answer is x = -1

Check:

`1 - (2)/(x+3) = (x+1)/(x-3)\\\\1 - (2)/(-1+3) = (-1+1)/(-1-3)\\\\1 - (2)/(2) = (0)/(-4)\\\\1 - 1 = 0\\\\0 = 0\\\\`

The answer is fully confirmed.

You can use a graphing tool like GeoGebra to visually confirm the answer.