How do you solve #4/(x^2  11x + 30)  7/(x^2 + x  30) = 11/ (x^2  36)#?
So:
Now we can rewrite the initial expression as
Bringing the left member to the right, we obtain the following equation:
A fraction equals zero if and only if the numerator is zero (of course the denominator cannot be zero, which we will check at the end). So, the equation reduces to
Expanding:
Summing:
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To solve the equation 4/(x^2  11x + 30)  7/(x^2 + x  30) = 11/(x^2  36), we can follow these steps:

Factor the denominators of each fraction: x^2  11x + 30 = (x  6)(x  5) x^2 + x  30 = (x + 6)(x  5) x^2  36 = (x  6)(x + 6)

Rewrite the equation with the factored denominators: 4/((x  6)(x  5))  7/((x + 6)(x  5)) = 11/((x  6)(x + 6))

Find a common denominator for all the fractions, which is (x  6)(x + 6)(x  5): 4(x + 6)/((x  6)(x + 6)(x  5))  7(x  6)/((x + 6)(x  5)(x  6)) = 11/((x  6)(x + 6))

Multiply both sides of the equation by the common denominator to eliminate the denominators: 4(x + 6)  7(x  6) = 11

Simplify and solve for x: 4x  24  7x + 42 = 11 11x + 18 = 11 11x = 7 x = 7/11
Therefore, the solution to the equation is x = 7/11.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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