# How do you find the vertical asymptotes #(x^2+4)/(6x-5x^2)#?

The answer would be got by equating denominator to zero and solving. Here it would be

The given function.

To find the Vertical Asymptotes factor both numerator and denominator first.

The numerator is not factorable.

The next step is to cancel the common factors if any from the numerator and denominator. In our problem there is none. This is done to eliminate holes

Finally, equate the factors remaining in the denominator to zero and solve.

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To find the vertical asymptotes of the function ( \frac{x^2 + 4}{6x - 5x^2} ), set the denominator equal to zero and solve for ( x ). The values of ( x ) obtained from this process will represent the vertical asymptotes of the function.

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To find the vertical asymptotes of ( \frac{x^2 + 4}{6x - 5x^2} ), set the denominator equal to zero and solve for ( x ).

(6x - 5x^2 = 0)

Factor out (x): (x(6 - 5x) = 0)

Set each factor equal to zero:

- (x = 0)
- (6 - 5x = 0)

Solve for (x) in the second equation: [6 - 5x = 0] [6 = 5x] [x = \frac{6}{5}]

So, the vertical asymptotes are (x = 0) and (x = \frac{6}{5}).

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When evaluating a one-sided 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 one-sided 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 one-sided 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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