Write a rational function with a vertical asymptote at x = 3, a horizontal asymptote at y = -2 and zeros at x = 1, -1.
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Hello!
To solve this, you are trying to convert one side to a quadratic equation and the other to just 0. Then, solve the equation.
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First, move the /2 to the other side of the equation.
(a+1)/2 = 1/a
a+1 = 2/a
Next, multiply both sides by a.
a+1 = 2/a
And then subtract both sides by 2. This will get you to a quadratic equation.
Now, factor the equation. When we're factoring, we are looking for the form (a + b)(a + c), where b + c must equal 1 (the coefficient of a) and b*c must equal -2. In this case, b = 2, and c = -1.
Therefore:
(a + 2)(a - 1) = 0
To get the answer, recall that anything multiplied by 0 is equal to 0. Therefore, to get the left side to equal 0, either (a + 2) or (a - 1) must equal 0. To do this, a must either be -2 or 1.
Therefore, a = -2, or a = 1.
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Check your work:
(-2 + 1)/2 = 1/-2
-1/2 = -1/2
(1 + 1)/2 = 1/1
2/2 = 1/1
1 = 1
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Hope this helps!