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snow_lady [41]
4 years ago
10

Which expression is equivalent to the following complex fraction?

Mathematics
2 answers:
jekas [21]4 years ago
3 0

Answer: last option.

Step-by-step explanation:

- Subtract the fractions that are in the numerator.

- Add the  fractions that are in the denominator.

Then:

\frac{\frac{1}{x}-\frac{1}{y}}{\frac{1}{x}+\frac{1}{y}}=\frac{\frac{y-x}{xy}}{\frac{y+x}{xy}}

- Multiply the numerator of the fraction on the top by the denomianator of the fraction on the bottom.

- Simplify.

Then:

=\frac{(y-x)(xy)}{(y+x)(xy)}=\frac{(y-x)}{(y+x)}

tatiyna4 years ago
3 0

Answer:

The correct answer is last option

Step-by-step explanation:

It is given that,

(1/x - 1/y)/(1/x +1/y)

<u>To simplify (1/x - 1/y)</u>

1/x - 1/y = (y - x)/xy

<u>To simplify (1/x - 1/y)</u>

1/x + 1/y = (y + x)/xy

To find equivalent expression

(1/x - 1/y)/(1/x +1/y = [(y - x)/xy]/[(y + x)/xy]

 = (y - x)*xy/(y +x)*xy = (y - x)/(y + x)

Therefore the correct answer is last option

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Solve for a: 5(a+5)-3=3(2-a)
ivann1987 [24]

Simplify:

5(a + 5) + -3 = 3(2 + -1a)

Reorder the terms:

5(5 + a) + -3 = 3(2 + -1a)

(5 * 5 + a * 5) + -3 = 3(2 + -1a)

(25 + 5a) + -3 = 3(2 + -1a)

Reorder the terms again:

25 + -3 + 5a = 3(2 + -1a)

Combine like terms:

]25 + -3 = 22

22 + 5a = 3(2 + -1a)

22 + 5a = (2 * 3 + -1a * 3)

22 + 5a = (6 + -3a)

Solve:

22 + 5a = 6 + -3a

To solve for variable 'a':

You have to move all terms containing A to the left, all other terms to the right.

Then add '3a' to each side of the equation:

22 + 5a + 3a = 6 + -3a + 3a

Combine like terms:

5a + 3a = 8a

22 + 8a = 6 + -3a + 3a

Combine like terms again:

-3a + 3a = 0

22 + 8a = 6 + 0

22 + 8a = 6

Add '-22' to each side of the equation.:

22 + -22 + 8a = 6 + -22

Combine like terms:

22 + -22 = 0

0 + 8a = 6 + -22

8a = 6 + -22

Combine like terms once more:

6 + -22 = -16

8a = -16

Divide each side by '8'.

a = -2

Simplify:

a = -2

Answer: a=-2

Hope I could help! :)

8 0
3 years ago
Read 2 more answers
A biker can cover a distance of 45 miles in 5 hours
Alexus [3.1K]

Answer:

9mph

Step-by-step explanation:

45 divided by 5= 9 which means she travel nine miles per hour.

Please mark brainlist! Im doing a challenge.

8 0
3 years ago
The volume of a rectangular prism is 2x^3 - 6x^2 + 8x , and the volume of a cube is 27x^3. What is the total volume of the prism
AleksAgata [21]

Answer:

\displaystyle V_{P + C} = 29x^3 - 6x^2 + 8x

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

Terms/Coefficients

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify.</em>

<em />\displaystyle V_P = 2x^3 - 6x^2 + 8x<em />

<em />\displaystyle V_C = 27x^3<em />

<em />

<u>Step 2: Find Combined Volume</u>

  1. [Set up] Add:                                                                                                     \displaystyle V_P + V_C = V_{P + C}
  2. Substitute in variables:                                                                                    \displaystyle V_{P + C} = 27x^3 + 2x^3 - 6x^2 + 8x
  3. Combine like terms:                                                                                        \displaystyle V_{P + C} = 29x^3 - 6x^2 + 8x
8 0
3 years ago
For problems 12 - 14, Determine whether each sequence appears to be an
marshall27 [118]

Step-by-step explanation:

⇒12)It is an arithmetic sequence.

   d=2-1=3-2=4-3=1

    a(n) = a +(n-1)d

    a(n) = 1+(n-1)1

The next three terms:

a(6) = 1+(6-1)1=6

a(7) = 1+(7-1)1=7

a(8) = 1+(8-1)1=8

⇒13)It is an arithmetic sequence.

   d=0-3=-3-0=-6+3=-3

    a(n) = a +(n-1)d

    a(n) = 3+(n-1)-3

The next three terms:

a(5) = 3+(5-1)-3=-9

a(6) = 3+(6-1)-3=-12

a(7) = 3+(7-1)-3=-15

⇒14)It is <u>not </u>an arithmetic sequence.

⇒15) a(50) = 10 +(50-1)5

                  =<u>255</u>

<u>I hope this helps</u>

<u />

8 0
3 years ago
SIMPLIFY. WILL MARK BRAINLIEST
Nikitich [7]

Here is your answer. x^5-3x^4+6x^2+x-9

5 0
3 years ago
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