Please help me with this problem-I'm stuck
(x-2)/(x+2) = (x+10)/x
I'm not even sure where to start-Thanks for any help you can provide
just cross-multiply
x(x-2) = (x+2)(x+10)
x^2 - 2x = x^2 + 12x + 20
-14x = 20
x = -20/14
x = -10/7
That is so easy-I can't believe I was screwing it up so badly-Thank you
To solve this equation, you can start by cross-multiplying and simplifying the equation. Here's a step-by-step explanation:
1. Start with the equation: (x-2)/(x+2) = (x+10)/x.
2. Cross-multiply by multiplying the numerator of the left side by the denominator of the right side and vice versa:
(x-2) * x = (x+10) * (x+2).
3. Simplify both sides of the equation to expand and distribute:
x^2 - 2x = x^2 + 12x + 20.
4. Now, you have a quadratic equation. Move all the terms to one side of the equation to set it equal to zero:
x^2 - 2x - (x^2 + 12x + 20) = 0.
5. Simplify further by combining like terms:
x^2 - 2x - x^2 - 12x - 20 = 0.
-14x - 20 = 0.
6. Finally, solve the equation:
-14x = 20.
x = 20 / -14 = -10 / 7.
Hence, the solution to the equation is x = -10 / 7.