Aneeka Hunt
2021-09-13
Answered

Write the given expression as a single quotient in which only positive exponents and/or radicals appear. Do NOT rationalize the denominator.

$\frac{\sqrt{4+x}-x\cdot \frac{1}{2\sqrt{4+x}}}{4+x}$

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hesgidiauE

Answered 2021-09-14
Author has **106** answers

Using cross multiplication on the numerator to simplify the numerator

$\frac{\sqrt{4+x}-x\cdot \frac{1}{2\sqrt{4+x}}}{4+x}$

Cross multiplying numerator

$\frac{\frac{\sqrt{4+x}\times 2\sqrt{4+x}-x}{2\sqrt{4+x}}}{4+x}$

$=\frac{2{\left(\sqrt{4+x}\right)}^{2}-x}{2\sqrt{4+x}\times (4+x)}$

$=\frac{2(4+x)-x}{2{(4+x)}^{\frac{3}{2}}}=\frac{4}{{(4+x)}^{\frac{3}{2}}}$

Cross multiplying numerator

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${e}^{-\tau}\le {e}^{-\tau /t}{t}^{-1}$

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for $t\in (0,1)$ and $0<\tau <t$ ?

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