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sqr(x^2-4)+(x^2)/x^2+1

I got ((x^2+1)*sqr(x^2-4)+x^2)/x^2+1

But my teacher gave (sqr(x^2-4)+x^2)/x^2+1

I did the problem over again but I can't figure out why my teacher got the answer. Can someone confirm that my teacher is right or am I right?

sqr=square root
^=to the power of
/=divided by
*=multiplied by

User Icon for Reiny Reiny answered
15 years ago

I get

[(x^2+1)√(x^2-4) + x^2]/(x^2 + 1)
which matches your answer.

User Icon for Explain Bot Explain Bot answered
11 months ago

To determine whether your answer or your teacher's answer is correct, we will simplify the expression step-by-step using the order of operations.

The given expression is:
sqrt(x^2 - 4) + (x^2 / x^2 + 1)

Step 1: Simplify the denominator
The denominator (x^2 / (x^2 + 1)) can be simplified. To do this, we need to factor out x^2 and write the expression as:
x^2 / x^2 * (x^2 + 1)

Step 2: Simplify the numerator
The numerator (sqrt(x^2 - 4)) can be simplified by factoring it out:
(sqrt(x^2 - 4)) * (x^2 + 1)

Step 3: Simplify further
Now we have:
(sqrt(x^2 - 4) * (x^2 + 1)) / (x^2 / x^2 * (x^2 + 1))

Step 4: Cancel out common factors
Notice that (x^2 + 1) appears in both the numerator and the denominator. We can cancel them out:
(sqrt(x^2 - 4) * (x^2 + 1)) / (x^2 / x^2 * (x^2 + 1))
= sqrt(x^2 - 4) / (x^2 / x^2)
= sqrt(x^2 - 4)

Therefore, the correct simplified form of the expression is sqrt(x^2 - 4). This means your teacher's answer is correct, and your initial answer, ((x^2 + 1) * sqrt(x^2 - 4) + x^2) / (x^2 + 1), is not simplified correctly.