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Lina20 [59]
3 years ago
12

Write the Rational Expression in simplest form.

exFormula1" title="\frac{x^2-x-6}{24-5x-x^2}" alt="\frac{x^2-x-6}{24-5x-x^2}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Liula [17]3 years ago
4 0

Answer:

-(x+2)/(x+8)

Step-by-step explanation:

( x^2 -x-6)

------------------

24 - 5x -x^2

Factor out a minus sign from the denominator

( x^2 -x-6)

------------------

-( x^2 +5x -24)

Factor the numerators and the denominators

( x-3) (x+2)

------------------

-( x+8)(x-3)

Cancel like terms

  x+2

------------------

-(x+8)

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5 0
2 years ago
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What is the solution to the equation
Dafna11 [192]
\sqrt{4t+5}=3-\sqrt{t+5}\\\\D:4t+5\geq0\ \wedge\ t+5\geq0\ \wedge\ \sqrt{t+5}\leq3\\\\t\geq-\dfrac{5}{4}\ \wedge\ t\geq-5\ \wedge\ t\leq6

therefore
D:x\in\left< -\dfrac{5}{4};\ 6\right>

\sqrt{4t+5}=3-\sqrt{t+5}\ \ \ |^2\\\\(\sqrt{4t+5})^2=(3-\sqrt{t+5})^2\ \ \ |use:(a-b)^2=a^2-2ab+b^2\\\\4t+5=3^2-2\cdot3\cdot\sqrt{t+5}+(\sqrt{t+5})^2\\\\4t+5=9-6\sqrt{t+5}+t+5\ \ \ \ |-t\\\\3t+5=14-6\sqrt{t+5}\ \ \ \ |-14\\\\3t-9=-6\sqrt{t+5}\ \ \ \ |change\ signs
9-3t=6\sqrt{t+5}\ \ \ \ |:3\\\\3-t=2\sqrt{t+5}\ \ \ \ |^2\\\\(3-t)^2=(2\sqrt{t+5})^2\\\\3^2-2\cdot3\cdot t+t^2=4(t+5)\\\\9-6t+t^2=4t+20\ \ \ |-4t-20\\\\t^2-10t-11=0\\\\t^2+t-11t-11=0\\\\t(t+1)-11(t+1)=0\\\\(t+1)(t-11)=0\iff t+1=0\ \vee\ t-11=0\\\\t=-1\in D\ \vee\ t=11\notin D
Answer: t = -1.


7 0
3 years ago
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h(0)=3

The diver begins 3 meters above the water

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\begin{gathered} h(1)=8 \\ 8>6.75>3 \end{gathered}

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