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Firlakuza [10]
1 year ago
13

Solve: x2 − x − 6/x2 = x − 6/2x + 2x + 12/x After multiplying each side of the equation by the LCD and simplifying, the resultin

g equation is .
Mathematics
1 answer:
Vesna [10]1 year ago
7 0

The resulting equation after simplyfing the given equation is 3x^2 + 20x + 12 = 0 and whoose solutions are x = -2/3 or x = -6.

According to the given question.

We have an equation

\frac{x^{2}-x-6 }{x^{2} } = \frac{x-6}{2x} +\frac{2x+12}{x}

So, to find the resulting equation of the above equation we need to simplify.

First we will take LCD

\frac{x^{2} -x - 6 }{x^{2} } = \frac{x -6+2(2x + 12)}{2x}

\implies \frac{x^{2}-x-6 }{x^{2} } =\frac{x-6+4x+24}{2x}

\implies \frac{x^{2}-x-6 }{x^{2} } = \frac{5x +18}{2x}

Multiply both the sides by x.

\frac{x^{2}-x-6 }{x} = \frac{5x+18}{2}

Again multiply both the sides by x

2x^{2} -2x-12 = 5x^{2} +18x

\implies 5x^{2} -2x^{2} +18x +2x +12 = 0

\implies 3x^{2} + 18x+2x + 12 = 0

Factorize the above equation

⇒3x(x+6)+2(x+6) = 0

⇒(3x + 2)(x+6) = 0

⇒ x = -2/3 or x = -6

Hence, the resulting equation after simplyfing the given equation is 3x^2 + 20x + 12 = 0 and whoose solutions are x = -2/3 or x = -6.

Find out more information about equation here:

brainly.com/question/2976807

#SPJ4

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F(x)=2x+3 and g(x)=4x-2. Find f(x) x g(x). Find f(x) - g(x).
const2013 [10]

Answer:

<u><em>f(x) * g(x) is </em></u><u><em>8x^2 + 8x -6</em></u>

<u><em>f(x) - g(x) is </em></u><u><em>-2x + 5</em></u>

Step-by-step explanation:

<u><em>When finding the answer, we can notice they already give the values for the needed answers.</em></u>

<u><em>The first one requires f(x) and g(x). At the beginning of the question it shows that </em></u><u><em>f(x) is equal to 2x+3. Meaning we can plug in 2x+3 for f(x).</em></u>

<u><em>The same goes for g(x). At the begginning of the question, it shows that </em></u><u><em>g(x) is equal to 4x-2. Meaning we can plug in 4x-2 for g(x).</em></u>

<u><em>f(x) * g(x)</em></u>

<u><em>(2x+3) * (4x-2)</em></u>

<u><em>To find the answer, we need to </em></u><u><em>distibute the 2x+3 into 4x-2</em></u><u><em>.</em></u>

<u><em>To distribute, we do </em></u><u><em>:</em></u>

<u><em>2x * (4x-2)   +   3 * (4x-2)</em></u>

<u><em>First we distribute the 2x</em></u>

<u><em>2x * 4x  =  8x^2        and        2x * -2  =  -4x</em></u>

<u><em>8x^2 - 4x</em></u>

<u><em>Next we distibute the 3</em></u>

<u><em>3 * 4x  =  12x        and        3 * -2 = -6</em></u>

<u><em>12x - 6</em></u>

<u><em>Now we can combine them by</em></u><u><em> adding like terms </em></u><u><em>to get the asnwer:</em></u>

<u><em>8x^2 = 8x^2</em></u>

<u><em>-4x + 12x = 8x</em></u>

<u><em>-6 = -6</em></u>

<u><em>The first answer is </em></u><u><em>8x^2 + 8x -6</em></u>

<u><em>Second question:</em></u>

<u><em>Since we already know the values for f(x) and g(x), all we have to do is </em></u><u><em>plug in the values</em></u><u><em>.</em></u>

<u><em>(2x+3) - (4x-2)</em></u>

<u><em>This time, since we are subtracting, all we have to do is </em></u><u><em>subtract like terms</em></u><u><em>.</em></u>

<u><em>2x - 4x = -2x</em></u>

<u><em>3 - (-2) = 5</em></u>

<u><em>The second answer is </em></u><u><em>-2x + 5</em></u>

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Step-by-step explanation:

In this question, we are tasked with calculating the volume of the rectangular prism.

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V = Base area * height

from the question, we have the base area as 12 square centimeters and the height as 3 centimeters.

Plugging these values into the equation, the value of the volume is thus 12 * 3 = 36 cubic centimeters

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