SOLUTION: Solve this quadratic equation, with ckecking: x/x+1 + 2/x=1

Question 349043: Solve this quadratic equation, with ckecking: 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

Proof, substitute -2 for x in your equation:

(-2)/(-2+1)+(2)/(-2)=1
Move the minus sign from the numerator to the front of the expression.
-(2)/(-2+1)+(2)/(-2)=1
Add 1 to -2 to get -1.
-(2)/(-1)+(2)/(-2)=1
Move the minus sign from the denominator to the front of the expression.
-(-(2)/(1))+(2)/(-2)=1
Any expression divided by 1 is the expression.
-(-2)+(2)/(-2)=1
Move the minus sign in the denominator to the front of the expression.
-(-2)-(2)/(2)=1
Reduce the expression -(2)/(2) by removing a factor of 2 from the numerator and denominator.
-(-2)-1=1
Multiply -1 by each term inside the parentheses.
2-1=1
Subtract 1 from 2 to get 1.
1=1
Since 1=1, the equation will always be true.
Always True
RELATED QUESTIONS
i need to solve this quadratic equation with checking: (x)/(x+1)+(2)/(x)=(1)... (answered by mananth)

Quadratic equation (x - 1)^2 = -49... (answered by checkley77)

solve this equation by using the quadratic form 3/x-7+4/x+2=1 (answered by Alan3354,Edwin McCravy)

Solve this equation by using the quadratic formula. 3/x-7+4/x+2=1 (answered by thesvw)

Please help with this equation. Solve using the quadratic formula: x^2-7x-1=-7 Thank... (answered by mangopeeler07)

I need help with this problem? Use the Quadratic Formula to solve the equation.... (answered by solver91311)

Solve this quadratic equation by Extracting square roots: 1. 1=1/3x^2 and 2.... (answered by oscargut)

Solve this equation for x with working:... (answered by funmath)

How do i solve this quadratic equation:... (answered by Alan3354)