(2-4i)+(3+7i)

+ (3 + 7i)" alt="(2 - 4i) + (3 + 7i)" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

zysi [14]4 years ago

5 0

$(2-4i)+(3+7i)=5+3i$

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Find the sum of \sqrt{4}√ 4 and 3\sqrt{9}3√ 9 in simplest form. also, determine whether the result is rational or ir

igomit [66]

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5 0

3 years ago

I need help with this problem.

sdas [7]

Answer:

$\text{4}\quad -3x^{-1}+x^{-2}$

Step-by-step explanation:

The answer choices suggest there is a common factor of (x+2) that can be removed from numerator and denominator.

The denominator factors as ...

$x^3+2x^2=x^2(x+2)$

The numerator obviously has no factors of x. We can try any of several means to determine if (x+2) is a factor. I tried synthetic division and found that the numerator can be written as ...

$-3x^2-5x+2=(-3x+1)(x+2)$

Then the expression simplifies to ...

$\dfrac{-3x^2-5x+2}{x^3+2x^2}=\dfrac{(-3x+1)(x+2)}{x^2(x+2)}\\\\=\dfrac{-3x+1}{x^2}=\dfrac{-3x}{x^2}+\dfrac{1}{x^2}=-3x^{-1}+x^{-2} \qquad\text{matches choice 4}$