Question 349040: Solve this equation: x/x+1 + 2/x=1
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! (x)/(x+1)+(2)/(x)=1
Find the LCD (least common denominator) of (x)/((x+1))+(2)/(x)+1.
Least common denominator: x(x+1)
Multiply each term in the equation by x(x+1) in order to remove all the denominators from the equation.
(x)/(x+1)*x(x+1)+(2)/(x)*x(x+1)=1*x(x+1)
Simplify the left-hand side of the equation by canceling the common factors.
x^(2)+2x+2=1*x(x+1)
Simplify the right-hand side of the equation by multiplying out all the terms.
x^(2)+2x+2=x^(2)+x
Move all terms not containing x to the right-hand side of the equation.
x^(2)+2x+2-x^(2)-x=0
Since x^(2) and -x^(2) are like terms, add -x^(2) to x^(2) to get 0.
0+2x+2-x=0
Since 2x and -x are like terms, add -x to 2x to get x.
x+2=0
Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides.
x=-2
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