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forsale [732]
3 years ago
11

An equivalent expression with a rational denominator is...

Mathematics
1 answer:
Whitepunk [10]3 years ago
4 0

Given the expression,

(8x-56x^2)/(\sqrt{14x-2})

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.

[(8x-56x^2)(\sqrt{14x-2})]/[(\sqrt{14x-2})(\sqrt{14x-2})]

If we have (\sqrt{a})(\sqrt{a}), we will get \sqrt{a^2} by multiplying them. And \sqrt{a^2} = a.

So here in the problem, we will get,

[(8x-56x^2)(\sqrt{14x-2})]/(14x-2)

Now in the numerator we have (8x-56x^2). We can check 8x is common there. we will take out -8x from it, we will get,

-8x(-1+7x)

-8x(7x-1)

And in the denominator we have 14x-2. We can check 2 is common there. If we take out 2 from it we will get,

2(7x-1)

So we can write the expression as

[(-8x)(7x-1)(\sqrt{14x-2})]/[2(7x-1)]

(7x-1) is common to the numerator and denominator both, if we cancel it we will get,

(-8x)(\sqrt{14x-2})/2

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

(-4x)(\sqrt{14x-2})

(-4x)(14x-2)^(1/2)

So we have got the required answer here.

The correct option is the last one.

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