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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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Alinara [238K]

-125x

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3 years ago
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Prove divisibility 45^45·15^15 by 75^30
Anuta_ua [19.1K]

Answer:

3^{75}

Step-by-step explanation:

We are asked to divide our given fraction: \frac{45^{45}*15^{15}}{75^{30}}.

We will simplify our division problem using rules of exponents.

Using product rule of exponents (a*b)^n=a^n*b^n we can write:

45^{45}=(3*15)^{45}=3^{45}*15^{45}

75^{30}=(5*15)^{30}=5^{30}*15^{30}

Substituting these values in our division problem we will get,

\frac{3^{45}*15^{45}*15^{15}}{5^{30}*15^{30}}

Using power rule of exponents a^m*a^n=a^{m+n} we will get,

\frac{3^{45}*15^{45+15}}{5^{30}*15^{30}}

\frac{3^{45}*15^{60}}{5^{30}*15^{30}}

Using quotient rule of exponent \frac{a^m}{a^n}=a^{m-n} we will get,

\frac{3^{45}*15^{60-30}}{5^{30}}

\frac{3^{45}*15^{30}}{5^{30}}

Using product rule of exponents (a*b)^n=a^n*b^n we will get,

\frac{3^{45}*(3*5)^{30}}{5^{30}}

\frac{3^{45}*3^{30}*5^{30}}{5^{30}}

Upon canceling out 5^{30} we will get,

3^{45}*3^{30}

Using power rule of exponents a^m*a^n=a^{m+n} we will get,

3^{45+30}

3^{75}

Therefore, our resulting quotient will be 3^{75}.

8 0
3 years ago
Pls pls i need help with this
Scrat [10]

Answer:

5+8=13

5/13

Lisa's fraction is 5/13

6 0
3 years ago
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NeTakaya

Answer:

(0-2i)(6-7i)

Step-by-step explanation:

The answer to this is pretty straightforward, as if you add a 0 to -2i, it will not change the expression.

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Find the difference between 45 2/3 and 27 1/2 . Express your answer in lowest terms
BARSIC [14]

45 2/3 - 27 1/2 = 18.

8 0
3 years ago
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