# Fraction with Radical - need to simplify (easy)

• mathatesme
In summary, the conversation is about simplifying the expression (sqrt(x) - 4) / (x - 16). The person is asking for an explanation and confirmation of their approach, which involves canceling out the (sqrt(x) - 4) in the numerator and denominator. The final answer is determined to be sqrt(x) + 4. The expert confirms that this approach is correct and also mentions an alternative way to simplify the expression.
mathatesme
This is probably easy for everyone on this forum but me. Can someone please explain this to me.

I need to simplify this:

(sqrt(x) - 4) / (x - 16))

am I on the right track by doing it this way...

(sqrt(x) - 4) / (sqrt(x) - 4) (sqrt(x) + 4) ...then cancel the (sqrt(x) - 4) in the Numerator and Denominator. To have my final answer be...

sqrt(x) + 4

You mean

$$\frac{1}{\sqrt{x}+4}$$

Daniel.

Okay...yeah...1/(sqrt(x)+4)

Is that correct?

And thank you for the fast reply!

Yes, that's correct.

$$x-16= (\sqrt{x}-4)(\sqrt{x}+4)$$

Thanks.

Thank you, I really appreciate your help! :)

## 1. How do I simplify a fraction with a radical?

To simplify a fraction with a radical, you need to first factor the number inside the radical. Then, you can look for any perfect squares that can be taken out of the radical. Divide the numerator and denominator by the square root of the perfect square to simplify the fraction.

## 2. Can I simplify a fraction with a radical if the numerator and denominator are both radicals?

Yes, you can still simplify a fraction with a radical if both the numerator and denominator are radicals. Follow the same steps as simplifying a fraction with one radical, but make sure to simplify each radical separately before dividing.

## 3. What if the fraction has a radical in the denominator?

If the fraction has a radical in the denominator, you can multiply both the numerator and denominator by the conjugate of the radical in the denominator. This will eliminate the radical in the denominator and make it easier to simplify the fraction.

## 4. Can I simplify a fraction with different types of radicals?

Yes, you can simplify a fraction with different types of radicals. The key is to factor each individual radical and look for any common factors that can be simplified. Then, you can combine the simplified radicals and continue simplifying the fraction.

## 5. Is there a specific order to simplify a fraction with a radical?

Yes, there is a specific order to simplify a fraction with a radical. First, simplify any coefficients or numbers outside of the radicals. Then, factor and simplify any radicals inside the numerator and denominator. Finally, simplify any remaining radicals in the fraction and combine like terms if necessary.

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