x+2/x+3=x-1/x+1. Solve the following equation for x. The solution is ?
Thank you for your help have worked this problem and ones like this for hours can't get the right answer:)
x + 2/x + 3 = x - 1/x + 1
It's usually helpful to get rid of denominators, so multiply both sides by x
x^2 + 2 + 3x = x^2 - 1 + x
subtract x^2 from both sides
2 + 3x = -1 + x
collect like terms
2x = -3
So, x = ?
Kay, can you see how important it is to use brackets to correctly show your equation.
Quidditch solved your equation correctly according to the way you typed it, but I have a suspicion that, since you worked on this "for hours", that you probably meant,
(x+2)/(x+3) = (x-1)/(x+1)
if so, then .... cross-multiply
(x+2)(x+1) = (x+3)(x-1)
take it from there, (Igot x = -5)
To solve the equation (x + 2)/(x + 3) = (x - 1)/(x + 1) for x, we need to eliminate the fractions by cross-multiplying.
Cross-multiplying involves multiplying the numerator of the left-hand side expression by the denominator of the right-hand side expression and vice versa. This gives us:
(x + 2)(x + 1) = (x - 1)(x + 3)
Now, let's simplify and expand each side of the equation:
(x^2 + 3x + 2x + 2) = (x^2 + 3x - x - 3)
Simplifying the equation further:
x^2 + 5x + 2 = x^2 + 2x - 3
Next, we can further simplify the equation by subtracting x^2 from both sides to get rid of the x^2 term:
5x + 2 = 2x - 3
Now, let's isolate the x term by subtracting 2x from both sides:
5x - 2x + 2 = -3
Combining like terms:
3x + 2 = -3
To isolate the x term, we can subtract 2 from both sides:
3x + 2 - 2 = -3 - 2
Simplifying:
3x = -5
Finally, divide both sides of the equation by 3 to solve for x:
3x/3 = -5/3
x = -5/3
Therefore, the solution to the equation (x + 2)/(x + 3) = (x - 1)/(x + 1) is x = -5/3.