Michaela is solving rational equations.
A. What is the solution set of the equation ...
x^2-7x+12 (all over or divided by) x^2+x-12 both equal to 3.
What I did first was factor both equations geting (x-4) on the top and (x+4) on the bottom both equal to 3. I am confused on what to do with the 3.
I checked the calculator online and the answer is said to be -8 but I don't know how they got that. Someone show me the steps. Thankyou.
So I read that as:
(x^2-7x+12)/(x^2+x-12) = 3
(x-3)(x-4)/((x+4)(x-3)) = 3
(x-4)/(x+4) = 3/1
cross-multiply
3x+12 = x-4
2x = -16
x = -8
To solve the rational equation (x^2-7x+12)/(x^2+x-12) = 3, the first step you took was correct - factoring the numerator and denominator to simplify the equation. You found that:
(x-4) / (x+4) = 3
Now, to solve for x, you can cross-multiply. This means multiplying the numerator of the left side (x-4) with the denominator of the right side (3), and multiplying the denominator of the left side (x+4) with the numerator of the right side (1):
(x-4) * 3 = (x+4) * 1
Now, distribute and simplify both sides of the equation:
3x - 12 = x + 4
Next, isolate the x terms on one side of the equation and the constant terms on the other side. You can do this by subtracting x from each side and adding 12 to each side:
2x = 16
Finally, divide both sides of the equation by 2 to solve for x:
x = 8
So, the solution to the rational equation is x = 8.
It looks like the calculator online gave you a different answer of x = -8. To figure out how they arrived at that answer, it would be helpful to see the steps or approach they used.