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leonid [27]
3 years ago
7

How would I solve this Rational Equation? Solve for all values of x.

Mathematics
1 answer:
Nesterboy [21]3 years ago
4 0

9514 1404 393

Answer:

  x = 4

Step-by-step explanation:

I like to put these in the form f(x) = 0. We can do that by subtracting the right side. Common factors can be cancelled from numerator and denominator, provided they are not zero.

  \dfrac{7}{x+3}+\dfrac{3}{x-3}-\dfrac{x}{x-3}=0\\\\ \dfrac{7(x-3)+(x+3)(3-x)}{(x+3)(x-3)}=0\\\\\dfrac{(x-3)(4-x)}{(x-3)(x+3)}=0\\\\ \dfrac{4-x}{x+3}=0\qquad x\ne3\\\\x=4 \qquad\text{equate the numerator to zero, add $x$}

_____

If you leave the numerator as (x-3)(4-x), then there are two values of x that make it zero. Because x=3 makes the equation "undefined", it cannot be considered to be a solution.

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20 subtracted from three times a number is 6 more than the number
kompoz [17]
<h3>20 subtracted from three times a number is 6 more than the number. Then the number is 13</h3>

<em><u>Solution:</u></em>

<em><u>Given statement is:</u></em>

20 subtracted from three times a number is 6 more than the number

We can translate the sentence into algebraic expression

Let "a" be the unknown number

Then,

20 subtracted from three times "a" is 6 more than "a"

Which means,

3a - 20 = 6 + a

3a - a = 6 + 20

2a = 26

Divide both sides by 2

a = 13

Thus the number is 13

3 0
3 years ago
Which of the following is the simplest form of this expression?
Softa [21]

Step-by-step explanation:

which expression there is no expression here

4 0
3 years ago
A jeweler wants to make 14 grams of an alloy that is precisely 75% gold.. The jeweler has alloys that are 25% gold, 50% gold, &a
Goryan [66]

Given that the jeweler has alloys that are 25% gold, 50% gold, and 82% gold.

As he wants to make 14 grams of an alloy by adding two different alloys that is precisely 75% gold, so one alloy must have a percentage of gold more than 75%.

One alloy is 82% gold and, the second can be chosen between 25% gold, 50% gold, so there are two cases.

Case 1: 82% gold + 50% gold

Let x grams of 82% gold and y  grams of 50% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 50% of y

\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times y \\\\

\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times (14-x)  [as x+y=14]

\Rightarrow 75 \times 14 = 82 \times x + 50 \times (14-x)  \\\\\Rightarrow 75 \times 14 = 82 \times x + 50 \times14-50\times x \\\\\Rightarrow 75 \times 14 = 32 \times x + 50 \times14 \\\\\Rightarrow 32 \times x =75 \times 14 - 50 \times14 \\\\

\Rightarrow x =(25 \times 14)/32=10.9375 grams

and y = 14-x= 14-10.9375=3.0625 grams.

Hence, 10.9375 grams of 82% gold and 3.0625  grams of 50% gold added to make 14 grams of 75% gold.

Case 2: 82% gold + 25% gold

Let x grams of 82% gold and y  grams of 25% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 25% of y

\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times y \\\\\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times (14-x) \\\\ \Rightarrow 75 \times 14 = 82 \times x + 25 \times (14-x)  \\\\\Rightarrow 75 \times 14 = 82 \times x + 25 \times14-25\times x \\\\\Rightarrow 75 \times 14 = 57 \times x + 25 \times14 \\\\\Rightarrow 57 \times x =75 \times 14 - 25 \times14 \\\\

\Rightarrow x =(50 \times 14)/57=12.28 grams

and y = 14-x= 14-12.28=1.72 grams.

Hence, 12.28 grams of 82% gold and 1.72  grams of 50% gold added to make 14 grams of 75% gold.

3 0
2 years ago
What is 9/12 simplified
Assoli18 [71]
9 and 12 have a common factor of 3 so 9/12 = 3/4
7 0
3 years ago
Read 2 more answers
it costs $31.28 to fill your gas tank, which holds 16 gallons. find the price per gallon to fill your gas tank.
tia_tia [17]

Answer:

1.955

Step-by-step explanation:

$31.28 ÷ 16 = 1.955

5 0
2 years ago
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