solve each equation:
x over x+1 plus 2= 3x over x+2
x/(x+1) + 2= 3x/(x+2)
multipy both sides by (x+1)(x+2)
x(x+2)+2(x+1)(x+2)=3x(x+1)
x^2+2x+2(x^2+3x+2)=3x^2+3x
x^2+2x+2x^2+6x+4=3x^2+3x
subtract 3x^2 from each side
8x+4=3x
now solve. check my work.
Thank you!!
To solve the equation, we need to find the value of x that satisfies the equation:
(x / (x + 1)) + 2 = (3x / (x + 2))
To eliminate the fractions, we can multiply all terms by the least common denominator, which in this case is (x + 1)(x + 2).
[(x + 1)(x + 2) * (x / (x + 1))] + 2 * (x + 1)(x + 2) = [(3x / (x + 2)) * (x + 1)(x + 2)]
After canceling out the common factors, we get:
x(x + 2) + 2(x + 1)(x + 2) = 3x(x + 1)
Expanding and simplifying:
x^2 + 2x + 2(x^2 + 3x + 2) = 3x^2 + 3x
x^2 + 2x + 2x^2 + 6x + 4 = 3x^2 + 3x
Combining like terms:
3x^2 - x^2 + 2x - 6x - 3x + 4 - 0 = 0
2x^2 - 7x + 4 = 0
This is now a quadratic equation, which can be solved by factoring, completing the square, or using the quadratic formula. In this case, we can factor it:
(2x - 1)(x - 4) = 0
Set each factor to zero and solve for x:
2x - 1 = 0
x = 1/2
x - 4 = 0
x = 4
Therefore, the solutions to the equation are x = 1/2 and x = 4.