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sattari [20]
4 years ago
8

Simplify the sum. State any restrictions on the variables.

Mathematics
1 answer:
Debora [2.8K]4 years ago
4 0

The sum is \frac{x+2}{x+3}.

Solution:

Given equation:

$\frac{x-2}{x+3}+\frac{10 x}{x^{2}-9}

        $=\frac{x-2}{x+3}+\frac{10 x}{x^{2}-3^2}

Using algebraic expression: a^2-b^2=(a-b)(a+b)

         $=\frac{x-2}{x+3}+\frac{10 x}{(x-3)(x+3)}

To make the denominator same, multiply and divide the first term by (x –3)

         $=\frac{(x-2)(x-3)}{(x+3)(x-3)}+\frac{10 x}{(x-3)(x+3)}

         $=\frac{(x-2)(x-3)+10x}{(x+3)(x-3)}

          $=\frac{x^2-2x-3x+6+10x}{(x+3)(x-3)}

         $=\frac{x^2+5x+6}{(x+3)(x-3)}

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

Cancel the common factors.

         $=\frac{x+2}{x+3}

$\frac{x-2}{x+3}+\frac{10 x}{x^{2}-9}=\frac{x+2}{x+3} ; but x ≠ –3

If you substitute x = –3, the value is indeterminate.

Hence the sum is \frac{x+2}{x+3}.

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Hey! I was wondering if someone could explain to me how solving two-step inequalities works. Thanks!
lina2011 [118]

Here is the inequality:

-2x+6

You're looking for x. To find it, you have to remove everything on the same side of the variable. The only thing with it is positive 6. To remove it, you have to do the opposite of it, which is -6, which is also the same as subtracting 6. Subtract 6 from both sides:

-2x+6-6

Now you have -2x. When you have a negative variable, the inequality sign changes. Change the sign:

-2x14

You're looking for x alone. To leave x alone, you have divide both sides by -2 since the variable is -2x. Divide both sides by -2:

-2x \div -2 > 14 \div -2 \\\\x>-7

When dividing a negative number number by a positive or vice versa, the result is ALWAYS negative. That's why in your answer, it's -7.

Your answer is x > -7

GRAPH:


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3 years ago
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I can’t see the photo is blurry
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3 years ago
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In a fruit salad there are 12 strawberries 11 grapes 9 kiwis and 4 papayas find the ratio of kiwis to the total of number of pie
ipn [44]

9/36

which would be simplified to 1/4

8 0
2 years ago
Help I don't think any of them is the correct answer!
pentagon [3]
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3 years ago
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Find the probability of having 2, 3, or 4
denis-greek [22]

Answer:

16% for 2 successes, 6.4% for 3 successes, 2.6% for 4 successes, and 1% for 5 successes

Step-by-step explanation:

Since the success rate of a binomial experiment is 40%, converted to 0.4, you get the equation of f(x) = (0.4)^x, for where x is the amount of successful experiments

For the success of 2 experiments:

f(2) = (0.4)^2

     =0.16 => 16%

For the success of 3 experiments:

f(3) = (0.4)^3

     = 0.064 => 6.4%

For the success of 4 experiments:

f(4) = (0.4)^4

     = 0.0256 => 2.56% => ~2.6

For the success of 5 experiments:

f(5) = (0.4)^5

     = 0.01024 => 1.024% => ~1%

Your welcome and comment if you have any questions :)

3 0
3 years ago
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