An equivalent expression with a rational denominator

Given the expression,

We will have to rationalize the denominator first. To rationalize the denominator we have to multiply the numerator and denominator both by the square root part of the denominator.

If we have , we will get by multiplying them. And .

So here in the problem, we will get,

Now in the numerator we have . We can check 8x is common there. we will take out -8x from it, we will get,

And in the denominator we have . We can check 2 is common there. If we take out 2 from it we will get,

So we can write the expression as

is common to the numerator and denominator both, if we cancel it we will get,

We can divide -8 by the denominator, as -8 os divisible by 2. By dividing them we will get,

So we have got the required answer here.

The correct option is the last one.