Mathematics: An equivalent expression with a rational denominator

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An equivalent expression with a rational denominator

Ответ:

GreenHerbz206

12.03.2022

Mathematics

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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An equivalent expression with a rational denominator

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